{"segment":[{"time":24,"part":[{"title":"L\u1ef1a ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang nh\u1ea5t","title_trans":"","temp":"multiple_choice","correct":[[4]],"list":[{"point":5,"ques":"<center><img src='https://www.luyenthi123.com/file/luyenthi123/lop8/toan/daiso/bai4/lv2/img\/2.jpg' \/><\/center>Bi\u1ec3u th\u1ee9c $\\dfrac{27}{64}{{\\left( 2x-3y \\right)}^{3}}$ c\u00f3 th\u1ec3 \u0111\u01b0\u1ee3c vi\u1ebft l\u1ea1i th\u00e0nh:","select":["A. ${{\\left( \\dfrac{3}{4}x-\\dfrac{9}{4}y \\right)}^{3}}$","B. ${{\\left( \\dfrac{1}{16}x-\\dfrac{9}{16}y \\right)}^{3}}$","C. ${{\\left( \\dfrac{3}{8}x-\\dfrac{9}{2}y \\right)}^{3}}$","D. ${{\\left( \\dfrac{3}{2}x-\\dfrac{9}{4}y \\right)}^{3}}$"],"hint":" Do $\\dfrac{27}{64}=\\left(\\dfrac{3}{4} \\right)^3$, ta vi\u1ebft bi\u1ec3u th\u1ee9c th\u00e0nh l\u1eadp ph\u01b0\u01a1ng c\u1ee7a m\u1ed9t hi\u1ec7u.","explain":"<span class='basic_left'>Ta c\u00f3: <br\/> $\\dfrac{27}{64}{{\\left( 2x-3y \\right)}^{3}}={{\\left( \\dfrac{3}{4} \\right)}^{3}}{{\\left( 2x-3y \\right)}^{3}}={{\\left[ \\dfrac{3}{4}\\left( 2x-3y \\right) \\right]}^{3}}={{\\left( \\dfrac{3}{2}x-\\dfrac{9}{4}y \\right)}^{3}}$ . <br\/><span class='basic_pink'> V\u1eady \u0111\u00e1p \u00e1n \u0111\u00fang l\u00e0 D.<\/span>","column":2}]}],"id_ques":451},{"time":24,"part":[{"title":"L\u1ef1a ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang nh\u1ea5t","title_trans":"","temp":"multiple_choice","correct":[[1]],"list":[{"point":5,"ques":"<center><img src='https://www.luyenthi123.com/file/luyenthi123/lop8/toan/daiso/bai4/lv2/img\/2.jpg' \/><\/center>Bi\u1ec3u th\u1ee9c $\\dfrac{1}{125}{{\\left( a-2b \\right)}^{3}}$ c\u00f3 th\u1ec3 \u0111\u01b0\u1ee3c vi\u1ebft l\u1ea1i th\u00e0nh:","select":["A. ${{\\left( \\dfrac{a}{5}-\\dfrac{2}{5}b \\right)}^{3}}$","B. ${{\\left( \\dfrac{a}{15}-\\dfrac{2}{15}b \\right)}^{3}}$","C. ${{\\left( \\dfrac{a}{5}-\\dfrac{2}{15}b \\right)}^{3}}$","D. ${{\\left( \\dfrac{a}{5}-10b \\right)}^{3}}$"],"hint":" Do $\\dfrac{1}{125}=\\left(\\dfrac{1}{5} \\right)^3$, ta vi\u1ebft bi\u1ec3u th\u1ee9c th\u00e0nh l\u1eadp ph\u01b0\u01a1ng c\u1ee7a m\u1ed9t hi\u1ec7u.","explain":"<span class='basic_left'>Ta c\u00f3: <br\/> $\\dfrac{1}{125}{{\\left( a-2b \\right)}^{3}}$$={{\\left( \\dfrac{1}{5} \\right)}^{3}}{{\\left( a-2b \\right)}^{3}}$$={{\\left[ \\dfrac{1}{5}\\left( a-2b \\right) \\right]}^{3}}$$={{\\left( \\dfrac{a}{5}-\\dfrac{2}{5}b \\right)}^{3}}$ . <br\/><span class='basic_pink'> V\u1eady \u0111\u00e1p \u00e1n \u0111\u00fang l\u00e0 A.<\/span>","column":2}]}],"id_ques":452},{"time":24,"part":[{"title":"L\u1ef1a ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang nh\u1ea5t","title_trans":"","temp":"multiple_choice","correct":[[2]],"list":[{"point":5,"ques":"Vi\u1ebft l\u1ea1i bi\u1ec3u th\u1ee9c sau th\u00e0nh d\u1ea1ng l\u1eadp ph\u01b0\u01a1ng c\u1ee7a m\u1ed9t t\u1ed5ng ho\u1eb7c m\u1ed9t hi\u1ec7u:<br\/> ${{x}^{3}}+2{{x}^{2}}z+\\dfrac{4}{3}x{{z}^{2}}+\\dfrac{8}{27}{{z}^{3}}$","select":["A. $\\left(x-\\dfrac{2}{3}z \\right)^3$","B. $\\left(x+\\dfrac{2}{3}z \\right)^3$","C. $\\left(x+\\dfrac{8}{27}z \\right)^3$","D. $\\left(x+\\dfrac{4}{3}z \\right)^3$"],"hint":"\u0110\u01b0a bi\u1ec3u th\u1ee9c v\u1ec1 l\u1eadp ph\u01b0\u01a1ng c\u1ee7a m\u1ed9t t\u1ed5ng: $(a+b)^3=a^3+3a^2b+3ab^2+b^3$.<br\/> T\u1eeb $x^3$ ta t\u00ecm ra $a$, t\u1eeb $\\dfrac{8}{27}{{z}^{3}}$ ta t\u00ecm ra $b$. ","explain":"<span class='basic_left'><span class='basic_green'>H\u01b0\u1edbng d\u1eabn:<\/span><br\/> <b>B\u01b0\u1edbc 1:<\/b> Ta nh\u1eadn \u0111\u1ecbnh \u0111\u01b0a bi\u1ec3u th\u1ee9c v\u1ec1 l\u1eadp ph\u01b0\u01a1ng c\u1ee7a m\u1ed9t t\u1ed5ng. <br\/> <b>B\u01b0\u1edbc 2:<\/b> T\u00ecm $a, b$ t\u1eeb $x^3$ v\u00e0 $\\dfrac{8}{27}{{z}^{3}}$. <br\/><span class='basic_green'>B\u00e0i gi\u1ea3i<\/span><br\/> ${{x}^{3}}+2{{x}^{2}}z+\\dfrac{4}{3}x{{z}^{2}}+\\dfrac{8}{27}{{z}^{3}}$$={{x}^{3}}+3.{{x}^{2}}.\\dfrac{2}{3}z+3.x.{{\\left( \\dfrac{2}{3}z \\right)}^{2}}$$+{{\\left( \\dfrac{2}{3}z \\right)}^{3}}$$={{\\left( x+\\dfrac{2}{3}z \\right)}^{3}}$ . <br\/><span class='basic_pink'> V\u1eady \u0111\u00e1p \u00e1n \u0111\u00fang l\u00e0 B.<\/span>","column":2}]}],"id_ques":453},{"time":24,"part":[{"title":"L\u1ef1a ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang nh\u1ea5t","title_trans":"","temp":"multiple_choice","correct":[[3]],"list":[{"point":5,"ques":"Vi\u1ebft l\u1ea1i bi\u1ec3u th\u1ee9c sau th\u00e0nh d\u1ea1ng l\u1eadp ph\u01b0\u01a1ng c\u1ee7a m\u1ed9t t\u1ed5ng ho\u1eb7c m\u1ed9t hi\u1ec7u:<br\/> $\\dfrac{1}{8}-\\dfrac{3}{2}y+6{{y}^{2}}-8{{y}^{3}}$","select":["A. $\\left(\\dfrac{1}{8}-2y \\right)^3$","B. $\\left(\\dfrac{1}{8}-8y \\right)^3$","C. $\\left(\\dfrac{1}{2}-2y \\right)^3$","D. $\\left(\\dfrac{1}{2}+2y \\right)^3$"],"hint":"\u0110\u01b0a bi\u1ec3u th\u1ee9c v\u1ec1 l\u1eadp ph\u01b0\u01a1ng c\u1ee7a m\u1ed9t hi\u1ec7u: $(a-b)^3=a^3-3a^2b+3ab^2-b^3$.<br\/> T\u1eeb $\\dfrac{1}{8}$ ta t\u00ecm ra $a$, $8{{y}^{3}}$ ta t\u00ecm ra $b$. ","explain":"<span class='basic_left'><span class='basic_green'>H\u01b0\u1edbng d\u1eabn:<\/span><br\/><b>B\u01b0\u1edbc 1:<\/b> Ta nh\u1eadn \u0111\u1ecbnh \u0111\u01b0a bi\u1ec3u th\u1ee9c v\u1ec1 l\u1eadp ph\u01b0\u01a1ng c\u1ee7a m\u1ed9t hi\u1ec7u. <br\/> <b>B\u01b0\u1edbc 2:<\/b> T\u00ecm $a, b$ t\u1eeb $\\dfrac{1}{8}$ v\u00e0 $8{{y}^{3}}$. <br\/><span class='basic_green'>B\u00e0i gi\u1ea3i<\/span><br\/> $\\dfrac{1}{8}-\\dfrac{3}{2}y+6{{y}^{2}}-8{{y}^{3}}$$={{\\left( \\dfrac{1}{2} \\right)}^{3}}-3.{{\\left( \\dfrac{1}{2} \\right)}^{2}}.2y+3.\\dfrac{1}{2}.{{\\left( 2y \\right)}^{2}}$$-{{\\left( 2y \\right)}^{3}}$$={{\\left( \\dfrac{1}{2}-2y \\right)}^{3}}$. <br\/><span class='basic_pink'> V\u1eady \u0111\u00e1p \u00e1n \u0111\u00fang l\u00e0 C.<\/span>","column":2}]}],"id_ques":454},{"time":24,"part":[{"title":"L\u1ef1a ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang nh\u1ea5t","title_trans":"","temp":"multiple_choice","correct":[[1]],"list":[{"point":5,"ques":"Vi\u1ebft l\u1ea1i bi\u1ec3u th\u1ee9c sau th\u00e0nh d\u1ea1ng l\u1eadp ph\u01b0\u01a1ng c\u1ee7a m\u1ed9t t\u1ed5ng ho\u1eb7c m\u1ed9t hi\u1ec7u:<br\/> $27-54z+36z^2-8z^3$","select":["A. $(3-2z)^3$","B. $(3+2z)^3$","C. $(9-2z)^3$","D. $(9-8z)^3$"],"hint":"\u0110\u01b0a bi\u1ec3u th\u1ee9c v\u1ec1 l\u1eadp ph\u01b0\u01a1ng c\u1ee7a m\u1ed9t hi\u1ec7u: $(a-b)^3=a^3-3a^2b+3ab^2-b^3$.<br\/> T\u1eeb $27$ ta t\u00ecm ra $a$, $8z^3$ ta t\u00ecm ra $b$. ","explain":"<span class='basic_left'><span class='basic_green'>H\u01b0\u1edbng d\u1eabn:<\/span><br\/> <b>B\u01b0\u1edbc 1:<\/b> Ta nh\u1eadn \u0111\u1ecbnh \u0111\u01b0a bi\u1ec3u th\u1ee9c v\u1ec1 l\u1eadp ph\u01b0\u01a1ng c\u1ee7a m\u1ed9t hi\u1ec7u. <br\/> <b>B\u01b0\u1edbc 2:<\/b> T\u00ecm $a, b$ t\u1eeb $27$ v\u00e0 $8z^3$<br\/><span class='basic_green'>B\u00e0i gi\u1ea3i<\/span><br\/> $27-54z+36{{z}^{2}}-8{{z}^{3}}$$={{3}^{3}}-{{3.3}^{2}}.2z+3.3.{{\\left( 2z \\right)}^{2}}-{{\\left( 2z \\right)}^{3}}$$={{\\left( 3-2z \\right)}^{3}}$<br\/><span class='basic_pink'> V\u1eady \u0111\u00e1p \u00e1n \u0111\u00fang l\u00e0 A.<\/span>","column":2}]}],"id_ques":455},{"time":24,"part":[{"title":"L\u1ef1a ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang nh\u1ea5t ","title_trans":"","temp":"multiple_choice","correct":[[2]],"list":[{"point":5,"ques":"<center><img src='https://www.luyenthi123.com/file/luyenthi123/lop8/toan/daiso/bai4/lv2/img\/5.jpg' \/><\/center>Gi\u00e1 tr\u1ecb c\u1ee7a bi\u1ec3u th\u1ee9c $B={{\\left( x-1 \\right)}^{3}}-x{{\\left( x-2 \\right)}^{2}}+7{{x}^{2}}+x+4$ kh\u00f4ng ph\u1ee5 thu\u1ed9c v\u00e0o $x$. \u0110\u00fang hay sai? ","select":["\u0110\u00fang","Sai"],"hint":"S\u1eed d\u1ee5ng c\u00e1c h\u1eb1ng \u0111\u1eb3ng th\u1ee9c \u0111\u1ec3 bi\u1ebfn \u0111\u1ed5i bi\u1ec3u th\u1ee9c \u0111\u00e3 cho, x\u00e9t k\u1ebft qu\u1ea3 thu \u0111\u01b0\u1ee3c c\u00f3 ch\u1ee9a $x$ hay kh\u00f4ng.<br\/> N\u1ebfu kh\u00f4ng ch\u1ee9a $x$ th\u00ec gi\u00e1 tr\u1ecb bi\u1ec3u th\u1ee9c kh\u00f4ng ph\u1ee5 thu\u1ed9c v\u00e0o $x$. ","explain":"<span class='basic_left'>Ta c\u00f3: <br\/>$ B=(x - 1)^3 - x(x - 2)^2 + 7x^2+x+4 \\\\ = (x - 1)^3 - x(x^2 - 4x + 4) + 7x^2 + x + 4 \\\\ = x^3 - 3x^2 + 3x - 1 - x^3 + 4x^2 - 4x + 7x^2 + x + 4 \\\\ = 8x^2 + 3$ <br\/>V\u1eady gi\u00e1 tr\u1ecb c\u1ee7a B ph\u1ee5 thu\u1ed9c v\u00e0o bi\u1ebfn $x$.<br\/> <span class='basic_pink'> V\u1eady \u0111\u00e1p \u00e1n l\u00e0: Sai.<\/span>","column":2}]}],"id_ques":456},{"time":24,"part":[{"title":"L\u1ef1a ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang nh\u1ea5t","title_trans":"","temp":"multiple_choice","correct":[[1]],"list":[{"point":5,"ques":"<center><img src='https://www.luyenthi123.com/file/luyenthi123/lop8/toan/daiso/bai4/lv2/img\/5.jpg' \/><\/center>Gi\u00e1 tr\u1ecb c\u1ee7a bi\u1ec3u th\u1ee9c $A={{\\left( a+2 \\right)}^{3}}-\\left( a+6 \\right)\\left( {{a}^{2}}+12 \\right)+64$ b\u1eb1ng $0$ v\u1edbi m\u1ecdi $a$. \u0110\u00fang hay sai? ","select":["\u0110\u00fang","Sai"],"hint":"S\u1eed d\u1ee5ng c\u00e1c h\u1eb1ng \u0111\u1eb3ng th\u1ee9c \u0111\u1ec3 bi\u1ebfn \u0111\u1ed5i bi\u1ec3u th\u1ee9c \u0111\u00e3 cho, x\u00e9t k\u1ebft qu\u1ea3 thu \u0111\u01b0\u1ee3c c\u00f3 b\u1eb1ng 0 hay kh\u00f4ng.","explain":"<span class='basic_left'>Ta c\u00f3: <br\/>$ A={{\\left( a+2 \\right)}^{3}}$$-\\left( a+6 \\right)\\left( {{a}^{2}}+12 \\right)+64 $<br\/>$ ={{a}^{3}}+3.{{a}^{2}}.2+3.a{{.2}^{2}}+{{2}^{3}}$$-\\left( {{a}^{3}}+12a+6{{a}^{2}}+72 \\right)+64 $<br\/>$={{a}^{3}}+6{{a}^{2}}+12a+8-{{a}^{3}}$$-12a-6{{a}^{2}}-72+64 $<br\/>$ =0 $ <br\/>V\u1eady gi\u00e1 tr\u1ecb c\u1ee7a $A$ b\u1eb1ng $0$ v\u1edbi m\u1ecdi $a$<br\/> <span class='basic_pink'> V\u1eady \u0111\u00e1p \u00e1n l\u00e0: \u0110\u00fang<\/span>","column":2}]}],"id_ques":457},{"time":24,"part":[{"title":"Ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang","title_trans":"","temp":"multiple_choice","correct":[[1]],"list":[{"point":5,"select":["A. $\\left[ \\begin{aligned} & y=\\dfrac{2}{3} \\\\ & y=1 \\\\ & y=\\dfrac{1}{3} \\\\ \\end{aligned} \\right. $","B. $\\left[ \\begin{aligned} & y=\\dfrac{-2}{3} \\\\ & y=1 \\\\ & y=\\dfrac{1}{3} \\\\ \\end{aligned} \\right. $","C. $\\left[ \\begin{aligned} & y=\\dfrac{-2}{3} \\\\ & y=1 \\\\ & y=\\dfrac{-1}{3} \\\\ \\end{aligned} \\right. $"],"ques":"<center><img src='https://www.luyenthi123.com/file/luyenthi123/lop8/toan/daiso/bai4/lv2/img\/4.jpg' \/><\/center>Bi\u1ebft $27y^3-54y^2+36y-8=3y-2$, gi\u00e1 tr\u1ecb c\u1ee7a $y$ l\u00e0 ?","hint":" \u0110\u01b0a v\u1ebf tr\u00e1i v\u1ec1 d\u1ea1ng: $[f(y)]^3$, $f(y)$ l\u00e0 bi\u1ec3u th\u1ee9c ch\u1ee9a $y$.","explain":"<span class='basic_left'><span class='basic_green'>H\u01b0\u1edbng d\u1eabn:<\/span><br\/><b>B\u01b0\u1edbc 1:<\/b> \u0110\u01b0a v\u1ebf tr\u00e1i v\u1ec1 d\u1ea1ng: $[f(y)]^3$, $f(y)$ l\u00e0 bi\u1ec3u th\u1ee9c ch\u1ee9a $y$.<br\/> <b>B\u01b0\u1edbc 2:<\/b> N\u1ebfu $n^3-n=0\\Leftrightarrow n(n^2-1)=0$ <br\/><span class='basic_green'>B\u00e0i gi\u1ea3i<\/span><br\/>Ta c\u00f3: <br\/>$ 27{{y}^{3}}-54{{y}^{2}}+36y-8=3y-2 $<br\/>$ {{\\left( 3y-2 \\right)}^{3}}=3y-2 $<br\/>${{\\left( 3y-2 \\right)}^{3}}-\\left( 3y-2 \\right)=0 $<br\/>$ \\left( 3y-2 \\right)\\left[ {{\\left( 3y-2 \\right)}^{2}}-1 \\right]=0 $<br\/>$ \\Leftrightarrow \\left[ \\begin{aligned} & 3y-2=0 \\\\ & {{\\left( 3y-2 \\right)}^{2}}-1=0 \\\\ \\end{aligned} \\right.$$\\Leftrightarrow \\left[ \\begin{aligned} & 3y=2 \\\\ & {{\\left( 3y-2 \\right)}^{2}}=1 \\\\ \\end{aligned} \\right.$$\\Leftrightarrow \\left[ \\begin{aligned} & y=\\dfrac{2}{3} \\\\ & 3y-2=1 \\\\ & 3y-2=-1 \\\\ \\end{aligned} \\right.$$\\Leftrightarrow \\left[ \\begin{aligned} & y=\\dfrac{2}{3} \\\\ & y=1 \\\\ & y=\\dfrac{1}{3} \\\\ \\end{aligned} \\right. $<\/span> "}]}],"id_ques":458},{"time":24,"part":[{"title":"\u0110i\u1ec1n k\u1ebft qu\u1ea3 v\u00e0o \u00f4 tr\u1ed1ng ","title_trans":"","temp":"fill_the_blank","correct":[[["4"]]],"list":[{"point":5,"width":40,"type_input":"","ques":"<center><img src='https://www.luyenthi123.com/file/luyenthi123/lop8/toan/daiso/bai4/lv2/img\/4.jpg' \/><\/center>Bi\u1ebft $a^3-3a^2+3a-28=0$, gi\u00e1 tr\u1ecb c\u1ee7a $a$ l\u00e0 _input_","hint":"\u0110\u01b0a v\u1ebf tr\u00e1i v\u1ec1 d\u1ea1ng: $[f(a)]^3-b^3$, $f(a)$ l\u00e0 bi\u1ec3u th\u1ee9c ch\u1ee9a $a, b$ l\u00e0 h\u1eb1ng s\u1ed1<br\/> N\u1ebfu $x^3=y^3$ th\u00ec $x = y$","explain":"<span class='basic_left'><span class='basic_green'>H\u01b0\u1edbng d\u1eabn:<\/span><br\/><b>B\u01b0\u1edbc 1:<\/b> \u0110\u01b0a v\u1ebf tr\u00e1i v\u1ec1 d\u1ea1ng: $[f(a)]^3-b^3$, $f(a)$ l\u00e0 bi\u1ec3u th\u1ee9c ch\u1ee9a $a, b$ l\u00e0 h\u1eb1ng s\u1ed1 <br\/> <b>B\u01b0\u1edbc 2:<\/b> N\u1ebfu $x^3=y^3$ th\u00ec $x = y$<br\/><span class='basic_green'>B\u00e0i gi\u1ea3i<\/span><br\/>Ta c\u00f3: <br\/> $ {{a}^{3}}-3{{a}^{2}}+3a-28=0 \\\\ \\Leftrightarrow {{a}^{3}}-3{{a}^{2}}+3a-1-27 =0 \\\\ \\Leftrightarrow {{\\left( a-1 \\right)}^{3}}-27 =0 \\\\ \\Leftrightarrow {{\\left( a-1 \\right)}^{3}} =27 \\\\ \\Leftrightarrow {{\\left( a-1 \\right)}^{3}} ={{3}^{3}} \\\\ \\Leftrightarrow a-1 =3 \\\\ \\Leftrightarrow a =4 $ <br\/> <span class='basic_pink'> V\u1eady s\u1ed1 c\u1ea7n \u0111i\u1ec1n v\u00e0o \u00f4 tr\u1ed1ng l\u00e0 $4$. <\/span><\/span> "}]}],"id_ques":459},{"time":24,"part":[{"title":"\u0110i\u1ec1n k\u1ebft qu\u1ea3 v\u00e0o \u00f4 tr\u1ed1ng ","title_trans":"","temp":"fill_the_blank","correct":[[["4"],["5"]]],"list":[{"point":5,"width":40,"type_input":"","input_hint":["frac","sqr"],"ques":"<center><img src='https://www.luyenthi123.com/file/luyenthi123/lop8/toan/daiso/bai4/lv2/img\/4.jpg' \/><\/center>Bi\u1ebft $(5x+1)^3-125=0$, gi\u00e1 tr\u1ecb c\u1ee7a $x$ l\u00e0 <div class=\"frac123\"><div class=\"ts\">_input_<\/div><div class=\"ms\">_input_<\/div><\/div>","hint":"\u0110\u01b0a v\u1ec1 d\u1ea1ng $a^3=b^3$ th\u00ec $a = b$ ","explain":"<span class='basic_left'><span class='basic_green'>H\u01b0\u1edbng d\u1eabn:<\/span><br\/><b>B\u01b0\u1edbc 1:<\/b> ph\u00e2n t\u00edch $125 =5^3$. <br\/><b>B\u01b0\u1edbc 2:<\/b> \u0110\u01b0a v\u1ec1 d\u1ea1ng $a^3=b^3$ th\u00ec $a = b$<br\/><span class='basic_green'>B\u00e0i gi\u1ea3i<\/span><br\/>Ta c\u00f3: <br\/> $ {{(5x+1)}^{3}}-125 =0 \\\\ \\Leftrightarrow {{\\left( 5x+1 \\right)}^{3}}=125 \\\\ \\Leftrightarrow {{(5x+1)}^{3}}={{5}^{3}} \\\\ \\Leftrightarrow 5x+1 =5 \\\\ \\Leftrightarrow 5x=4 \\\\ \\Leftrightarrow x =\\dfrac{4}{5} $<\/span> "}]}],"id_ques":460},{"time":24,"part":[{"title":"\u0110i\u1ec1n k\u1ebft qu\u1ea3 v\u00e0o \u00f4 tr\u1ed1ng ","title_trans":"","temp":"fill_the_blank","correct":[[["8"],["27"]]],"list":[{"point":5,"width":40,"type_input":"","input_hint":["frac","sqr"],"ques":"<center><img src='https://www.luyenthi123.com/file/luyenthi123/lop8/toan/daiso/bai4/lv2/img\/5.jpg' \/><\/center> Gi\u00e1 tr\u1ecb c\u1ee7a bi\u1ec3u th\u1ee9c $8{{x}^{3}}-8{{x}^{2}}+\\dfrac{8}{3}x-\\dfrac{8}{27}$ v\u1edbi $x =\\dfrac{2}{3}$ l\u00e0 <div class=\"frac123\"><div class=\"ts\">_input_<\/div><div class=\"ms\">_input_<\/div><\/div>","hint":"R\u00fat g\u1ecdn bi\u1ec3u th\u1ee9c v\u1ec1 d\u1ea1ng l\u1eadp ph\u01b0\u01a1ng c\u1ee7a m\u1ed9t hi\u1ec7u. <br\/> Sau \u0111\u00f3 thay $x =\\dfrac{2}{3}$ v\u00e0o r\u1ed3i t\u00ednh.","explain":"<span class='basic_left'>Ta c\u00f3: <br\/>$8{{x}^{3}}-8{{x}^{2}}+\\dfrac{8}{3}x-\\dfrac{8}{27} \\\\ ={{\\left( 2x \\right)}^{3}}-3.{{\\left( 2x \\right)}^{2}}.\\dfrac{2}{3}+3.2x.{{\\left( \\dfrac{2}{3} \\right)}^{2}}-{{\\left( \\dfrac{2}{3} \\right)}^{3}} \\\\ ={{\\left( 2x-\\dfrac{2}{3} \\right)}^{3}}$.<br\/> Thay $x =\\dfrac{2}{3}$ v\u00e0o bi\u1ec3u th\u1ee9c sau khi r\u00fat g\u1ecdn, ta \u0111\u01b0\u1ee3c: <br\/> ${{\\left( 2.\\dfrac{2}{3}-\\dfrac{2}{3} \\right)}^{3}}$$={{\\left( \\dfrac{2}{3} \\right)}^{3}}=\\dfrac{8}{27}$ <\/span> "}]}],"id_ques":461},{"time":24,"part":[{"title":"\u0110i\u1ec1n k\u1ebft qu\u1ea3 v\u00e0o \u00f4 tr\u1ed1ng ","title_trans":"","temp":"fill_the_blank","correct":[[["8"]]],"list":[{"point":5,"width":40,"type_input":"","ques":"<center><img src='https://www.luyenthi123.com/file/luyenthi123/lop8/toan/daiso/bai4/lv2/img\/3.jpg' \/><\/center> Gi\u00e1 tr\u1ecb c\u1ee7a bi\u1ec3u th\u1ee9c ${{x}^{3}}-9{{x}^{2}}+27x-27$ v\u1edbi $x = 5$ l\u00e0 _input_","hint":"R\u00fat g\u1ecdn bi\u1ec3u th\u1ee9c v\u1ec1 d\u1ea1ng l\u1eadp ph\u01b0\u01a1ng c\u1ee7a m\u1ed9t hi\u1ec7u. <br\/> Sau \u0111\u00f3 thay $x = 5$ v\u00e0o r\u1ed3i t\u00ednh.","explain":"<span class='basic_left'>Ta c\u00f3: <br\/> $\\begin{align} & {{x}^{3}}-9{{x}^{2}}+27x-27 \\\\ & ={{x}^{3}}-3.{{x}^{2}}.3+3.x{{.3}^{2}}-{{3}^{3}} \\\\ & ={{\\left( x-3 \\right)}^{3}} \\\\ \\end{align}$ .<br\/> Thay $x = 5$ v\u00e0o bi\u1ec3u th\u1ee9c sau khi thu g\u1ecdn, ta \u0111\u01b0\u1ee3c: <br\/> ${{\\left( 5-3 \\right)}^{3}}={{\\left( 2 \\right)}^{3}}=8$ <br\/> <span class='basic_pink'> V\u1eady s\u1ed1 c\u1ea7n \u0111i\u1ec1n v\u00e0o \u00f4 tr\u1ed1ng l\u00e0 $8$ <\/span><\/span> "}]}],"id_ques":462},{"time":24,"part":[{"title":"\u0110i\u1ec1n k\u1ebft qu\u1ea3 v\u00e0o \u00f4 tr\u1ed1ng ","title_trans":"","temp":"fill_the_blank","correct":[[["64"]]],"list":[{"point":5,"width":40,"type_input":"","ques":"<center><img src='https://www.luyenthi123.com/file/luyenthi123/lop8/toan/daiso/bai4/lv2/img\/1.png' \/><\/center>Gi\u00e1 tr\u1ecb c\u1ee7a bi\u1ec3u th\u1ee9c $8{{z}^{3}}+24xz^2+24x^2z+8x^3$ v\u1edbi $x = z = 1$ l\u00e0 _input_","hint":"R\u00fat g\u1ecdn bi\u1ec3u th\u1ee9c v\u1ec1 d\u1ea1ng l\u1eadp ph\u01b0\u01a1ng c\u1ee7a m\u1ed9t t\u1ed5ng. <br\/> Sau \u0111\u00f3 thay $x = z = 1$ v\u00e0o \u0111\u1ec3 t\u00ednh.","explain":"<span class='basic_left'> Ta r\u00fat g\u1ecdn: <br\/> $ 8{{z}^{3}}+24x{{z}^{2}}+24{{x}^{2}}z+8{{x}^{3}} $<br\/>$ ={{\\left( 2z \\right)}^{3}}+3.{{\\left( 2z \\right)}^{2}}.2x+3.2z.{{\\left( 2x \\right)}^{2}}$$+{{\\left( 2x \\right)}^{3}} $<br\/>$ ={{\\left( 2z+2x \\right)}^{3}} $ <br\/> Thay $x = z = 1$ v\u00e0o bi\u1ec3u th\u1ee9c sau khi thu g\u1ecdn, ta \u0111\u01b0\u1ee3c: <br\/> $ {{\\left( 2.1+2.1 \\right)}^{3}}={{4}^{3}}=64$ <br\/> <span class='basic_pink'> V\u1eady s\u1ed1 c\u1ea7n \u0111i\u1ec1n v\u00e0o \u00f4 tr\u1ed1ng l\u00e0 $64$ <\/span><\/span> "}]}],"id_ques":463},{"time":24,"part":[{"title":"\u0110i\u1ec1n d\u1ea5u $+$ ho\u1eb7c $-$ v\u00e0o \u00f4 tr\u1ed1ng \u0111\u1ec3 \u0111\u01b0\u1ee3c m\u1ed9t khai tri\u1ec3n \u0111\u00fang ","title_trans":"","temp":"fill_the_blank","correct":[[["-"],["-"]]],"list":[{"point":5,"width":40,"type_input":"","ques":"<center><img src='https://www.luyenthi123.com/file/luyenthi123/lop8/toan/daiso/bai4/lv2/img\/3.jpg' \/><\/center>$27{{y}^{3}}\\FormInput[40][bl_elm_true basic_elm basic_blank basic_blank_part]{}9{{y}^{2}}+y-\\dfrac{1}{27}$$={{\\left( 3y\\FormInput[40][bl_elm_true basic_elm basic_blank basic_blank_part]{}\\dfrac{1}{3} \\right)}^{3}}$ ","hint":"Ta nh\u00ecn nh\u1eadn th\u1ea5y v\u1ebf tr\u00e1i c\u00f3 $-\\dfrac{1}{27}$ n\u00ean khai tri\u1ec3n tr\u00ean l\u00e0 c\u1ee7a h\u1eb1ng \u0111\u1eb3ng th\u1ee9c th\u1ee9 n\u0103m. <br\/> T\u1eeb khai tri\u1ec3n h\u1eb1ng \u0111\u1eb3ng th\u1ee9c th\u1ee9 n\u0103m ta t\u00ecm \u0111\u01b0\u1ee3c d\u1ea5u c\u1ea7n \u0111i\u1ec1n v\u00e0o \u00f4 tr\u1ed1ng.","explain":" <span class='basic_left'>Ta c\u00f3: <br\/> $27{{y}^{3}}-9{{y}^{2}}+y-\\dfrac{1}{27}$$={{\\left( 3y-\\dfrac{1}{3} \\right)}^{3}}$ <br\/> <span class='basic_pink'>V\u1eady d\u1ea5u c\u1ea7n \u0111i\u1ec1n v\u00e0o \u00f4 tr\u1ed1ng l\u00e0 d\u1ea5u $-$ v\u00e0 $-$<\/span> "}]}],"id_ques":464},{"time":24,"part":[{"title":"\u0110i\u1ec1n d\u1ea5u $+$ ho\u1eb7c $-$ v\u00e0o \u00f4 tr\u1ed1ng \u0111\u1ec3 \u0111\u01b0\u1ee3c m\u1ed9t khai tri\u1ec3n \u0111\u00fang ","title_trans":"","temp":"fill_the_blank","correct":[[["-"]]],"list":[{"point":5,"width":40,"type_input":"","ques":"<center><img src='https://www.luyenthi123.com/file/luyenthi123/lop8/toan/daiso/bai4/lv2/img\/4.jpg' \/><\/center>$8{{x}^{3}}-8{{x}^{2}}+\\dfrac{8}{3}x-\\dfrac{8}{27}$$={{\\left( 2x\\FormInput[40][bl_elm_true basic_elm basic_blank basic_blank_part]{}\\dfrac{2}{3} \\right)}^{3}}$ ","hint":"V\u1ebf tr\u00e1i l\u00e0 khai tri\u1ec3n h\u1eb1ng \u0111\u1eb3ng th\u1ee9c l\u1eadp ph\u01b0\u01a1ng c\u1ee7a m\u1ed9t hi\u1ec7u.","explain":"<span class='basic_left'>X\u00e9t v\u1ebf tr\u00e1i: $8{{x}^{3}}-8{{x}^{2}}+\\dfrac{8}{3}x-\\dfrac{8}{27}$ l\u00e0 khai tri\u1ec3n c\u1ee7a h\u1eb1ng \u0111\u1eb3ng th\u1ee9c th\u1ee9 n\u0103m. <br\/> Ta c\u00f3: <br\/> $8{{x}^{3}}-8{{x}^{2}}+\\dfrac{8}{3}x-\\dfrac{8}{27}={{\\left( 2x \\right)}^{3}}-3.{{\\left( 2x \\right)}^{2}}.\\dfrac{2}{3}+3.2x.{{\\left( \\dfrac{2}{3} \\right)}^{2}}-{{\\left( \\dfrac{2}{3} \\right)}^{3}}={{\\left( 2x-\\dfrac{2}{3} \\right)}^{3}}$<br\/> <span class='basic_pink'>V\u1eady d\u1ea5u c\u1ea7n \u0111i\u1ec1n v\u00e0o \u00f4 tr\u1ed1ng l\u00e0 d\u1ea5u $-$<\/span><\/span> "}]}],"id_ques":465},{"time":24,"part":[{"title":"\u0110i\u1ec1n d\u1ea5u + ho\u1eb7c - v\u00e0o \u00f4 tr\u1ed1ng \u0111\u1ec3 \u0111\u01b0\u1ee3c m\u1ed9t khai tri\u1ec3n \u0111\u00fang ","title_trans":"","temp":"fill_the_blank","correct":[[["-"],["+"],["-"]]],"list":[{"point":5,"width":40,"type_input":"","ques":"<center><img src='https://www.luyenthi123.com/file/luyenthi123/lop8/toan/daiso/bai4/lv2/img\/5.jpg' \/><\/center> ${{\\left( 1-3z \\right)}^{3}}$$=1\\FormInput[40][bl_elm_true basic_elm basic_blank basic_blank_part]{}9z\\FormInput[40][bl_elm_true basic_elm basic_blank basic_blank_part]{}27{{z}^{2}}$$\\FormInput[40][bl_elm_true basic_elm basic_blank basic_blank_part]{}27{{z}^{3}}$ ","hint":"V\u1ebf tr\u00e1i l\u00e0 l\u1eadp ph\u01b0\u01a1ng c\u1ee7a m\u1ed9t hi\u1ec7u, do \u0111\u00f3 ta khai tri\u1ec3n theo h\u1eb1ng \u0111\u1eb3ng th\u1ee9c \u0111\u1ec3 t\u00ecm c\u00e1c d\u1ea5u c\u1ea7n \u0111i\u1ec1n.","explain":"<span class='basic_left'>Ta c\u00f3: <br\/> ${{\\left( 1-3z \\right)}^{3}}=1-3.1.3z+3.1.{{\\left( 3z \\right)}^{2}}-{{\\left( 3z \\right)}^{3}}=1-9z+27{{z}^{2}}-27{{z}^{3}}$ <br\/> <span class='basic_pink'> V\u1eady d\u1ea5u c\u1ea7n \u0111i\u1ec1n v\u00e0o \u00f4 tr\u1ed1ng l\u1ea7n l\u01b0\u1ee3t l\u00e0 c\u00e1c d\u1ea5u $-, +$ v\u00e0 $\u2013$ <\/span><\/span> "}]}],"id_ques":466},{"time":24,"part":[{"title":"\u0110i\u1ec1n v\u00e0o \u00f4 tr\u1ed1ng \u0111\u1ec3 \u0111\u01b0\u1ee3c m\u1ed9t khai tri\u1ec3n \u0111\u00fang ","title_trans":"","temp":"fill_the_blank","correct":[[["2y"],["8"],["27"]]],"list":[{"point":5,"width":40,"type_input":"","ques":"<center><img src='https://www.luyenthi123.com/file/luyenthi123/lop8/toan/daiso/bai4/lv2/img\/5.jpg' \/><\/center>${{\\left( \\dfrac{2}{3}+\\FormInput[40][bl_elm_true basic_elm basic_blank basic_blank_part]{} \\right)}^{3}}$$=\\dfrac{\\FormInput[40][bl_elm_true basic_elm basic_blank basic_blank_part]{}}{\\FormInput[40][bl_elm_true basic_elm basic_blank basic_blank_part]{}}+\\dfrac{8}{3}y+8{{y}^{2}}+8{{y}^{3}}$ ","hint":"\u0110\u00e2y l\u00e0 khai tri\u1ec3n theo h\u1eb1ng \u0111\u1eb3ng th\u1ee9c: $(a+b)^3=a^3+3a^2b+3ab^2+b^3$.<br\/> Ta t\u00ednh $(\\dfrac{2}{3})^3$ v\u00e0 $8y^3=(...)^3$","explain":"<span class='basic_left'><span class='basic_green'>H\u01b0\u1edbng d\u1eabn:<\/span><br\/>\u0110\u00e2y l\u00e0 khai tri\u1ec3n theo h\u1eb1ng \u0111\u1eb3ng th\u1ee9c: $(a+b)^3=a^3+3a^2b+3ab^2+b^3$.<br\/> T\u00ednh $(\\dfrac{2}{3})^3$ v\u00e0 $8y^3=(...)^3$ <br\/><span class='basic_green'>B\u00e0i gi\u1ea3i<\/span><br\/>Ta c\u00f3: <br\/> ${{\\left( \\dfrac{2}{3}+2y \\right)}^{3}}$$={{\\left( \\dfrac{2}{3} \\right)}^{3}}+3.{{\\left( \\dfrac{2}{3} \\right)}^{2}}.2y+3.\\dfrac{2}{3}.{{\\left( 2y \\right)}^{2}}$$+{{\\left( 2y \\right)}^{3}}$$=\\dfrac{8}{27}+\\dfrac{8}{3}y+8{{y}^{2}}+8{{y}^{3}}$<br\/> <span class='basic_pink'>V\u1eady c\u1ea7n \u0111i\u1ec1n l\u00e0 $2y$ v\u00e0 $\\dfrac{8}{27}$ . <\/span><\/span> "}]}],"id_ques":467},{"time":24,"part":[{"title":"\u0110i\u1ec1n v\u00e0o \u00f4 tr\u1ed1ng \u0111\u1ec3 \u0111\u01b0\u1ee3c m\u1ed9t khai tri\u1ec3n \u0111\u00fang ","title_trans":"","temp":"fill_the_blank","correct":[[["1"],["2"]]],"list":[{"point":5,"width":40,"type_input":"","input_hint":["frac","sqr"],"ques":"<center><img src='https://www.luyenthi123.com/file/luyenthi123/lop8/toan/daiso/bai4/lv2/img\/1.png' \/><\/center>${{y}^{3}}-\\dfrac{3}{2}{{y}^{2}}+\\dfrac{3}{4}y-\\dfrac{1}{8}$$=( y-$ <div class=\"frac123\"><div class=\"ts\">_input_<\/div><div class=\"ms\">_input_<\/div><\/div>$)^3$","hint":"X\u00e9t v\u1ebf tr\u00e1i, khai tri\u1ec3n theo h\u1eb1ng \u0111\u1eb3ng th\u1ee9c: $(a-b)^3=a^3-3a^2b+3ab^2-b^3$.<br\/> T\u1eeb \u0111\u00f3 t\u00ecm \u0111\u01b0\u1ee3c y\u1ebfu t\u1ed1 c\u1ea7n \u0111i\u1ec1n v\u00e0o \u00f4 tr\u1ed1ng.","explain":"<span class='basic_left'><span class='basic_green'>H\u01b0\u1edbng d\u1eabn:<\/span><br\/><b>B\u01b0\u1edbc 1:<\/b> X\u00e9t v\u1ebf tr\u00e1i, khai tri\u1ec3n theo h\u1eb1ng \u0111\u1eb3ng th\u1ee9c: $(a-b)^3=a^3-3a^2b+3ab^2-b^3$. <br\/> <b>B\u01b0\u1edbc 2:<\/b> T\u1eeb \u0111\u00f3 t\u00ecm \u0111\u01b0\u1ee3c y\u1ebfu t\u1ed1 c\u1ea7n \u0111i\u1ec1n v\u00e0o \u00f4 tr\u1ed1ng. <br\/><span class='basic_green'>B\u00e0i gi\u1ea3i<\/span><br\/>Ta c\u00f3: <br\/> ${{y}^{3}}-\\dfrac{3}{2}{{y}^{2}}+\\dfrac{3}{4}y-\\dfrac{1}{8}$$={{y}^{3}}-3.{{y}^{2}}.\\dfrac{1}{2}+3.y.{{\\left( \\dfrac{1}{2} \\right)}^{2}}-{{\\left( \\dfrac{1}{2} \\right)}^{3}}$$={{\\left( y-\\dfrac{1}{2} \\right)}^{3}}$<\/span> "}]}],"id_ques":468},{"time":24,"part":[{"title":"L\u1ef1a ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang nh\u1ea5t","title_trans":"","temp":"multiple_choice","correct":[[1]],"list":[{"point":5,"ques":"<center><img src='https://www.luyenthi123.com/file/luyenthi123/lop8/toan/daiso/bai4/lv2/img\/2.jpg' \/><\/center>Khai tri\u1ec3n ${{\\left( \\dfrac{1}{2}-2z \\right)}^{3}}$ theo h\u1eb1ng \u0111\u1eb3ng th\u1ee9c ta \u0111\u01b0\u1ee3c:","select":["A. $\\dfrac{1}{8}-\\dfrac{3}{2}z+6{{z}^{2}}-8{{z}^{3}}$ ","B. $-\\dfrac{1}{8}+\\dfrac{3}{2}z-6{{z}^{2}}+8{{z}^{3}}$ ","C. $\\dfrac{1}{8}-8z^3$","D. $\\dfrac{1}{4}-3z+z^3$"],"hint":"Khai tri\u1ec3n theo h\u1eb1ng \u0111\u1eb3ng th\u1ee9c: $(a-b)^3=a^3-3a^2b+3ab^2-b^3$.","explain":"<span class='basic_left'><span class='basic_green'>H\u01b0\u1edbng d\u1eabn<\/span><br\/> Khai tri\u1ec3n theo h\u1eb1ng \u0111\u1eb3ng th\u1ee9c: $(a-b)^3=a^3-3a^2b+3ab^2-b^3$.<br\/><span class='basic_green'>Gi\u1ea3i<\/span><br\/><span class='basic_left'>Ta c\u00f3:<br\/> ${{\\left( \\dfrac{1}{2}-2z \\right)}^{3}}$$={{\\left( \\dfrac{1}{2} \\right)}^{3}}-3.{{\\left( \\dfrac{1}{2} \\right)}^{2}}.2z$$+3.\\dfrac{1}{2}.{{\\left( 2z \\right)}^{2}}-{{\\left( 2z \\right)}^{3}}$$=\\dfrac{1}{8}-\\dfrac{3}{2}z+6{{z}^{2}}-8{{z}^{3}}$ <span><br\/> <span class='basic_pink'> V\u1eady \u0111\u00e1p \u00e1n l\u00e0 A<\/span>","column":2}]}],"id_ques":469},{"time":24,"part":[{"title":"L\u1ef1a ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang nh\u1ea5t","title_trans":"","temp":"multiple_choice","correct":[[2]],"list":[{"point":5,"ques":"<center><img src='https://www.luyenthi123.com/file/luyenthi123/lop8/toan/daiso/bai4/lv2/img\/2.jpg' \/><\/center>Khai tri\u1ec3n ${{\\left( x+2y\\right)}^{3}}$ theo h\u1eb1ng \u0111\u1eb3ng th\u1ee9c ta \u0111\u01b0\u1ee3c:","select":["A. $x^3+8y^3$ ","B. $x^3+6x^2y+12xy^2+8y^3$ ","C. $x^2+4xy+4y^2$","D. $x^3+6xy+8y^3$"],"hint":"Khai tri\u1ec3n theo h\u1eb1ng \u0111\u1eb3ng th\u1ee9c: $(a+b)^3=a^3+3a^2b+3ab^2+b^3$.","explain":"<span class='basic_left'><span class='basic_green'>H\u01b0\u1edbng d\u1eabn<\/span><br\/> Khai tri\u1ec3n theo h\u1eb1ng \u0111\u1eb3ng th\u1ee9c: $(a+b)^3=a^3+3a^2b+3ab^2+b^3$.<br\/><span class='basic_green'>Gi\u1ea3i<\/span><br\/><span class='basic_left'>Ta khai tri\u1ec3n:<br\/> ${{\\left( x+2y \\right)}^{3}}$$={{x}^{3}}+3.{{x}^{2}}.2y+3.x.{{\\left( 2y \\right)}^{2}}+{{\\left( 2y \\right)}^{3}}$$={{x}^{3}}+6{{x}^{2}}y+12x{{y}^{2}}+8{{y}^{3}}$ <span><br\/> <span class='basic_pink'> V\u1eady \u0111\u00e1p \u00e1n l\u00e0 B.<\/span>","column":2}]}],"id_ques":470}],"lesson":{"save":0,"level":2}}