{"segment":[{"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/bai3/lv2/img\/1.png' \/><\/center>Khai tri\u1ec3n $(4y-1)^2$ theo h\u1eb1ng \u0111\u1eb3ng th\u1ee9c ta \u0111\u01b0\u1ee3c:","select":["A. $4y^2-8y+1$ ","B. $16y^2-8y+1$ ","C. $4y^2-4y+1$","D. $16y^2-4y+1$"],"hint":"Khai tri\u1ec3n theo h\u1eb1ng \u0111\u1eb3ng th\u1ee9c b\u00ecnh ph\u01b0\u01a1ng c\u1ee7a m\u1ed9t hi\u1ec7u","explain":"<span class='basic_left'>Ta c\u00f3:<br\/> $(4y-1)^2=(4y)^2-2.4y.1+1=16y^2-8y+1$<span><br\/> <span class='basic_pink'> V\u1eady \u0111\u00e1p \u00e1n l\u00e0 B.<\/span>","column":2}]}],"id_ques":401},{"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/bai3/lv2/img\/1.png' \/><\/center>Bi\u1ec3u th\u1ee9c $A=24x-18-9x^2$ lu\u00f4n d\u01b0\u01a1ng v\u1edbi m\u1ecdi $x$. \u0110\u00fang hay sai? ","select":["\u0110\u00fang","Sai"],"hint":"\u0110\u01b0a bi\u1ec3u th\u1ee9c $A$ v\u1ec1 d\u1ea1ng: $A=[f(x)]^2+a$ v\u1edbi $a$ l\u00e0 h\u1eb1ng s\u1ed1, $f(x)$ l\u00e0 bi\u1ec3u th\u1ee9c ch\u1ee9a bi\u1ebfn $x$. <br\/> Sau \u0111\u00f3 \u0111\u00e1nh gi\u00e1 $A$ c\u00f3 lu\u00f4n d\u01b0\u01a1ng hay kh\u00f4ng.","explain":"<span class='basic_left'> Ta c\u00f3: <br\/> $\\begin{align} & A=24x-18-9{{x}^{2}} \\\\ & =-\\left( 9{{x}^{2}}-24x+18 \\right) \\\\ & =-\\left[ {{\\left( 3x \\right)}^{2}}-2.3x.4+{{4}^{2}}-{{4}^{2}}+18 \\right] \\\\ & =-\\left[ {{\\left( 3x-4 \\right)}^{2}}+2 \\right] \\\\ \\end{align}$ <br\/>Do ${{\\left( 3x-4 \\right)}^{2}}\\ge 0$$ (\\forall x), \\Rightarrow {{\\left( 3x-4 \\right)}^{2}}+2\\,\\,\\,>\\,\\,0$$\\Rightarrow -\\left[ {{\\left( 3x-4 \\right)}^{2}}+2 \\right]\\,\\,<\\,\\,0$ <br\/>V\u1eady $A$ lu\u00f4n \u00e2m v\u1edbi m\u1ecdi $x$.<br\/> <span class='basic_pink'> V\u1eady \u0111\u00e1p \u00e1n l\u00e0: Sai.<\/span>","column":2}]}],"id_ques":402},{"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/bai3/lv2/img\/1.png' \/><\/center>Bi\u1ec3u th\u1ee9c $A=(x-8)(x-10)+3$ lu\u00f4n d\u01b0\u01a1ng v\u1edbi m\u1ecdi $x$. \u0110\u00fang hay sai? ","select":["\u0110\u00fang","Sai"],"hint":"\u0110\u01b0a bi\u1ec3u th\u1ee9c $A$ v\u1ec1 d\u1ea1ng: $A=[f(x)]^2+a$ v\u1edbi $a$ l\u00e0 h\u1eb1ng s\u1ed1, $f(x)$ l\u00e0 bi\u1ec3u th\u1ee9c ch\u1ee9a bi\u1ebfn $x$. <br\/> Sau \u0111\u00f3 \u0111\u00e1nh gi\u00e1 $A$ c\u00f3 lu\u00f4n d\u01b0\u01a1ng hay kh\u00f4ng.","explain":"<span class='basic_left'>Ta c\u00f3: <br\/> $\\begin{align} & A=\\left( x-8 \\right)\\left( x-10 \\right)+3 \\\\ & ={{x}^{2}}-10x-8x+80+3 \\\\ & ={{x}^{2}}-18x+83 \\\\ & =\\left( {{x}^{2}}-2.x.9+{{9}^{2}} \\right)-{{9}^{2}}+83 \\\\ & ={{\\left( x-9 \\right)}^{2}}+2\\,\\ge \\,\\,2\\,\\,>\\,\\,0, (\\forall x) \\\\ \\end{align}$ <br\/>V\u1eady $A$ lu\u00f4n d\u01b0\u01a1ng v\u1edbi m\u1ecdi $x$.<br\/> <span class='basic_pink'> V\u1eady \u0111\u00e1p \u00e1n l\u00e0 \u0110\u00fang.<\/span>","column":2}]}],"id_ques":403},{"time":24,"part":[{"title":"\u0110i\u1ec1n k\u1ebft qu\u1ea3 \u0111\u00fang nh\u1ea5t v\u00e0o \u00f4 tr\u1ed1ng","title_trans":"","temp":"fill_the_blank","correct":[[["7"],["2"]]],"list":[{"point":5,"width":40,"content":"","type_input":"","ques":"Gi\u00e1 tr\u1ecb l\u1edbn nh\u1ea5t c\u1ee7a $B=4x-x^2+3$ l\u00e0 _input_ t\u1ea1i $x$ = _input_","hint":"","explain":"<span class='basic_left'><span class='basic_green'>H\u01b0\u1edbng d\u1eabn:<\/span><br\/> <b> B\u01b0\u1edbc 1: <\/b> \u0110\u01b0a bi\u1ec3u th\u1ee9c $B$ v\u1ec1 d\u1ea1ng: $B=b-[f(x)]^2$ v\u1edbi $b$ l\u00e0 h\u1eb1ng s\u1ed1, $f(x)$ l\u00e0 bi\u1ec3u th\u1ee9c ch\u1ee9a bi\u1ebfn $x$. <br\/> <b> B\u01b0\u1edbc 2: <\/b> Sau \u0111\u00f3 \u0111\u00e1nh gi\u00e1: $B=b-[f(x)]^2\\le b$ <br\/> <b> B\u01b0\u1edbc 3: <\/b> K\u1ebft lu\u1eadn gi\u00e1 tr\u1ecb l\u1edbn nh\u1ea5t c\u1ee7a $B$, \u0111\u1ea1t \u0111\u01b0\u1ee3c khi n\u00e0o. <br\/> <span class='basic_green'>B\u00e0i gi\u1ea3i::<\/span><br\/>Ta c\u00f3:<br\/> $B=4x-x^2+3 \\\\ =-(x^2-4x-3) \\\\ =-(x^2-2.x.2+2^2-2^2-3) \\\\ =-[(x-2)^2-7] \\\\ =7-(x-2)^2$.<br\/> Ta th\u1ea5y: $7-(x-2)^2\\le 7$ v\u1edbi $\\forall x$ <br\/> Gi\u00e1 tr\u1ecb l\u1edbn nh\u1ea5t c\u1ee7a $B$ l\u00e0 $7$.<br\/> \u0110\u1ea1t \u0111\u01b0\u1ee3c khi $x-2=0 \\Leftrightarrow x=2$ .<br\/> <span class='basic_pink'> V\u1eady c\u1ea7n \u0111i\u1ec1n v\u00e0o \u00f4 tr\u1ed1ng l\u00e0 $7$ v\u00e0 $2$.<\/span>"}]}],"id_ques":404},{"time":24,"part":[{"title":"\u0110i\u1ec1n k\u1ebft qu\u1ea3 \u0111\u00fang nh\u1ea5t v\u00e0o \u00f4 tr\u1ed1ng","title_trans":"","temp":"fill_the_blank","correct":[[["-1"]]],"list":[{"point":5,"width":40,"content":"","type_input":"","ques":"Gi\u00e1 tr\u1ecb l\u1edbn nh\u1ea5t c\u1ee7a $B=-9x^2+12x-5$ l\u00e0 _input_","hint":"","explain":"<span class='basic_left'><span class='basic_green'>H\u01b0\u1edbng d\u1eabn:<\/span><br\/><b> B\u01b0\u1edbc 1: <\/b> \u0110\u00e1nh gi\u00e1 bi\u1ec3u th\u1ee9c B: $B=b-[f(x)]^2$ v\u1edbi $b$ l\u00e0 h\u1eb1ng s\u1ed1, $f(x)$ l\u00e0 bi\u1ec3u th\u1ee9c ch\u1ee9a bi\u1ebfn $x$.<br\/><b> B\u01b0\u1edbc 2: <\/b>Sau \u0111\u00f3 \u0111\u00e1nh gi\u00e1: $B=b-[f(x)]^2\\le b$,<br\/> <b> B\u01b0\u1edbc 3: <\/b> K\u1ebft lu\u1eadn gi\u00e1 tr\u1ecb l\u1edbn nh\u1ea5t c\u1ee7a $B$, \u0111\u1ea1t \u0111\u01b0\u1ee3c khi n\u00e0o. <br\/> <span class='basic_green'>B\u00e0i gi\u1ea3i::<\/span><br\/>Ta c\u00f3:<br\/> $\\begin{align} B&=-9x^2+12x-5\\\\&=-(9x^2-12x+5)\\\\&=-[(3x)^2-2.3x.2+2^2-2^2+5] \\\\&=-[(3x-2)^2+1] \\\\&=-1-(3x-2)^2 \\le -1, (\\forall x ) \\\\ \\end{align}$ <br\/> Gi\u00e1 tr\u1ecb l\u1edbn nh\u1ea5t c\u1ee7a $B$ l\u00e0 $-1$.<br\/> \u0110\u1ea1t \u0111\u01b0\u1ee3c khi $3x-2=0 \\Leftrightarrow x = \\dfrac{2}{3}$ .<br\/> <span class='basic_pink'> V\u1eady c\u1ea7n \u0111i\u1ec1n v\u00e0o \u00f4 tr\u1ed1ng l\u00e0 $-1$.<\/span>"}]}],"id_ques":405},{"time":24,"part":[{"title":"\u0110i\u1ec1n k\u1ebft qu\u1ea3 \u0111\u00fang nh\u1ea5t v\u00e0o \u00f4 tr\u1ed1ng","title_trans":"","temp":"fill_the_blank","correct":[[["1"]]],"list":[{"point":5,"width":40,"content":"","type_input":"","ques":"Gi\u00e1 tr\u1ecb nh\u1ecf nh\u1ea5t c\u1ee7a $A=4x^2+4x+2$ l\u00e0 _input_","hint":"","explain":"<span class='basic_left'><span class='basic_green'>H\u01b0\u1edbng d\u1eabn:<\/span><br\/> <b> B\u01b0\u1edbc 1: <\/b> \u0110\u01b0a bi\u1ec3u th\u1ee9c $A$ v\u1ec1 d\u1ea1ng: $A=[f(x)]^2+a$ v\u1edbi $a$ l\u00e0 h\u1eb1ng s\u1ed1, $f(x)$ l\u00e0 bi\u1ec3u th\u1ee9c ch\u1ee9a bi\u1ebfn $x$. <br\/> <b> B\u01b0\u1edbc 2: <\/b> \u0110\u00e1nh gi\u00e1: $A=[f(x)]^2+a\\ge a$,<br\/> <b> B\u01b0\u1edbc 3: <\/b> K\u1ebft lu\u1eadn gi\u00e1 tr\u1ecb nh\u1ecf nh\u1ea5t c\u1ee7a $A$, \u0111\u1ea1t \u0111\u01b0\u1ee3c khi n\u00e0o. <br\/> <span class='basic_green'>B\u00e0i gi\u1ea3i::<\/span><br\/>Ta nh\u1eadn th\u1ea5y:<br\/> $A=4x^2+4x+2 \\\\ =(2x)^2+2.2x.1+1^2+1 \\\\ =(2x+1)^2+1\\ge 1, \\hspace{0,2cm} (\\forall x )$ <br\/> Gi\u00e1 tr\u1ecb nh\u1ecf nh\u1ea5t c\u1ee7a $A$ l\u00e0 $1$.<br\/> \u0110\u1ea1t \u0111\u01b0\u1ee3c khi $2x+1=0 \\Leftrightarrow x = \\dfrac{-1}{2}$ .<br\/> <span class='basic_pink'> V\u1eady c\u1ea7n \u0111i\u1ec1n v\u00e0o \u00f4 tr\u1ed1ng l\u00e0 $1$.<\/span>"}]}],"id_ques":406},{"time":24,"part":[{"title":"\u0110i\u1ec1n k\u1ebft qu\u1ea3 \u0111\u00fang nh\u1ea5t v\u00e0o \u00f4 tr\u1ed1ng","title_trans":"","temp":"fill_the_blank","correct":[[["1"],["10"]]],"list":[{"point":5,"width":40,"content":"","type_input":"","ques":"Gi\u00e1 tr\u1ecb nh\u1ecf nh\u1ea5t c\u1ee7a $A=x^2-20x+101$ l\u00e0 _input_ t\u1ea1i $x$ =_input_","hint":"\u0110\u01b0a bi\u1ec3u th\u1ee9c $A$ v\u1ec1 d\u1ea1ng: $A=[f(x)]^2+a$ v\u1edbi $a$ l\u00e0 h\u1eb1ng s\u1ed1, $f(x)$ l\u00e0 bi\u1ec3u th\u1ee9c ch\u1ee9a bi\u1ebfn $x$. Sau \u0111\u00f3 t\u00ecm gi\u00e1 tr\u1ecb nh\u1ecf nh\u1ea5t c\u1ee7a $A$.","explain":"<span class='basic_left'><span class='basic_green'>H\u01b0\u1edbng d\u1eabn:<\/span><br\/> <b> B\u01b0\u1edbc 1: <\/b> \u0110\u01b0a bi\u1ec3u th\u1ee9c $A$ v\u1ec1 d\u1ea1ng: $A=[f(x)]^2+a$ v\u1edbi $a$ l\u00e0 h\u1eb1ng s\u1ed1, $f(x)$ l\u00e0 bi\u1ec3u th\u1ee9c ch\u1ee9a bi\u1ebfn $x$. <br\/> <b> B\u01b0\u1edbc 2: <\/b> Sau \u0111\u00f3 \u0111\u00e1nh gi\u00e1: $A=[f(x)]^2+a\\ge a$,<br\/> <b> B\u01b0\u1edbc 3: <\/b> K\u1ebft lu\u1eadn gi\u00e1 tr\u1ecb nh\u1ecf nh\u1ea5t c\u1ee7a $A$, \u0111\u1ea1t \u0111\u01b0\u1ee3c khi n\u00e0o. <br\/> <span class='basic_green'>B\u00e0i gi\u1ea3i::<\/span><br\/>Ta nh\u1eadn th\u1ea5y:<br\/> $A=x^2-20x+101 =x^2-2.x.10+10^2+1 =(x-10)^2+1\\ge 1$ v\u1edbi $\\forall x$ <br\/> Gi\u00e1 tr\u1ecb nh\u1ecf nh\u1ea5t c\u1ee7a $A$ l\u00e0 $1$.<br\/> \u0110\u1ea1t \u0111\u01b0\u1ee3c khi $x-10=0 \\Leftrightarrow x = 10$ .<br\/> <span class='basic_pink'> V\u1eady c\u1ea7n \u0111i\u1ec1n v\u00e0o \u00f4 tr\u1ed1ng l\u00e0 $1$ v\u00e0 $10$.<\/span>"}]}],"id_ques":407},{"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":"Bi\u1ebft $25x^2-10x+1=0$, gi\u00e1 tr\u1ecb c\u1ee7a $x$ l\u00e0:","select":["A. $2$","B. $5$","C. $\\dfrac{1}{2}$","D. $\\dfrac{1}{5}$"],"hint":"","explain":"<span class='basic_left'><span class='basic_green'>H\u01b0\u1edbng d\u1eabn:<\/span><br\/>V\u1ebf tr\u00e1i l\u00e0 khai tri\u1ec3n c\u1ee7a h\u1eb1ng \u0111\u1eb3ng th\u1ee9c th\u1ee9 hai, \u0111\u01b0a v\u1ec1 b\u00ecnh ph\u01b0\u01a1ng c\u1ee7a m\u1ed9t hi\u1ec7u v\u00e0 t\u00ecm $x$ .<br\/><span class='basic_green'>B\u00e0i gi\u1ea3i::<\/span><br\/> Ta c\u00f3: <br\/> $ 25x^2-10x+1=0\\\\ \\Leftrightarrow (5x-1)^2=0\\\\ \\Leftrightarrow 5x-1=0\\\\ \\Leftrightarrow x=\\dfrac{1}{5}$ <br\/><span class='basic_pink'> V\u1eady \u0111\u00e1p \u00e1n \u0111\u00fang l\u00e0 D.<\/span>","column":2}]}],"id_ques":408},{"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":"Bi\u1ebft $(2a-3)(2a+3)=0$, gi\u00e1 tr\u1ecb c\u1ee7a $a$ l\u00e0:","select":["A. $\\pm \\dfrac{3}{2}$","B. $\\pm \\dfrac{2}{3}$","C. $\\pm 3$","D. $\\pm 2$"],"hint":"N\u1ebfu $a.b = 0$ th\u00ec $a = 0$ ho\u1eb7c $b = 0$.","explain":"<span class='basic_left'> $\\begin{aligned} & \\left( 2a-3 \\right)\\left( 2a+3 \\right)=0 \\\\ & \\Leftrightarrow \\left[ \\begin{aligned} & 2a-3=0 \\\\ & 2a+3=0 \\\\ \\end{aligned} \\right.\\Leftrightarrow \\left[ \\begin{aligned} & a=\\dfrac{3}{2} \\\\ & a=-\\dfrac{3}{2} \\\\ \\end{aligned} \\right. \\\\ \\end{aligned}$ <br\/><span class='basic_pink'> V\u1eady \u0111\u00e1p \u00e1n \u0111\u00fang l\u00e0 A.<\/span>","column":2}]}],"id_ques":409},{"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":"Bi\u1ebft $y^2-4y+4=0$, gi\u00e1 tr\u1ecb c\u1ee7a $y$ l\u00e0:","select":["A. $2$","B. $4$","C. $\\dfrac{1}{2}$","D. $\\dfrac{1}{4}$"],"hint":"","explain":"<span class='basic_left'><span class='basic_green'>H\u01b0\u1edbng d\u1eabn:<\/span><br\/>V\u1ebf tr\u00e1i l\u00e0 khai tri\u1ec3n c\u1ee7a h\u1eb1ng \u0111\u1eb3ng th\u1ee9c th\u1ee9 hai, \u0111\u01b0a v\u1ec1 b\u00ecnh ph\u01b0\u01a1ng c\u1ee7a m\u1ed9t hi\u1ec7u v\u00e0 t\u00ecm $y$ .<\/span> <br\/><br\/><span class='basic_green'>B\u00e0i gi\u1ea3i:<\/span><br\/> Ta c\u00f3: <br\/> $ y^2-4y+4=0\\\\ \\Leftrightarrow (y-2)^2 =0\\\\ \\Leftrightarrow y-2 =0\\\\ \\Leftrightarrow y =2$ <br\/><span class='basic_pink'> V\u1eady \u0111\u00e1p \u00e1n \u0111\u00fang l\u00e0 A.<\/span>","column":2}]}],"id_ques":410},{"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/bai3/lv2/img\/1.png' \/><\/center>T\u00ednh nhanh (kh\u00f4ng d\u00f9ng m\u00e1y t\u00ednh): 2010.1990","select":["A. $3999990$","B. $3999900$","C. $2999900$","D. $2999990$"],"hint":"T\u00e1ch: $2010=2000+10$; $1999=2000-10$.","explain":"<span class='basic_left'><span class='basic_green'>H\u01b0\u1edbng d\u1eabn<\/span><br\/> <b> B\u01b0\u1edbc 1: <\/b> T\u00e1ch: $2010=2000+10$; $1999=2000-10$. <br\/> <b> B\u01b0\u1edbc 2: <\/b> Theo h\u1eb1ng \u0111\u1eb3ng th\u1ee9c th\u1ee9 ba, ta suy ng\u01b0\u1ee3c l\u1ea1i: $(a+b)(a-b)=a^2-b^2$ \u0111\u1ec3 t\u00ednh.<br\/><span class='basic_green'>Gi\u1ea3i<\/span><br\/> Ta c\u00f3: <br\/>$2010.1990 =(2000+10)(2000-10) =2000^2-10^2=4000000-100 =3999900$. <span><br\/> <span class='basic_pink'> V\u1eady \u0111\u00e1p \u00e1n l\u00e0 B.<\/span>","column":2}]}],"id_ques":411},{"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":"<center><img src='https://www.luyenthi123.com/file/luyenthi123/lop8/toan/daiso/bai3/lv2/img\/1.png' \/><\/center>T\u00ednh nhanh (kh\u00f4ng d\u00f9ng m\u00e1y t\u00ednh): $1001^2$","select":["A. $2002$","B. $1001001$","C. $1002001$","D. $2002002$"],"hint":"T\u00e1ch: $1001^2=(1000+1)^2$.","explain":"<span class='basic_left'><span class='basic_green'>H\u01b0\u1edbng d\u1eabn: <\/span><br\/> <b> B\u01b0\u1edbc 1: <\/b> Ta t\u00e1ch: $1001^2=(1000+1)^2$. <br\/> <b> B\u01b0\u1edbc 2: <\/b> Khai tri\u1ec3n theo h\u1eb1ng \u0111\u1eb3ng th\u1ee9c th\u1ee9 nh\u1ea5t: $(a+b)^2=a^2+2ab+b^2$ \u0111\u1ec3 t\u00ednh.<br\/><span class='basic_green'>B\u00e0i gi\u1ea3i<\/span><br\/><span class='basic_left'>Ta c\u00f3: <br\/>$1001^2=(1000+1)^2 \\\\ =1000^2+2.1000.1+1^2 \\\\ =1000000+2000+1 \\\\ =1002001$. <span><br\/> <span class='basic_pink'> V\u1eady \u0111\u00e1p \u00e1n l\u00e0 C.<\/span>","column":2}]}],"id_ques":412},{"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/bai3/lv2/img\/1.png' \/><\/center>T\u00ednh nhanh (kh\u00f4ng d\u00f9ng m\u00e1y t\u00ednh): $999^2$","select":["A. $998001$","B. $998000$","C. $1998$","D. $999999$"],"hint":"T\u00e1ch: $999^2=(1000-1)^2$.","explain":"<span class='basic_left'><span class='basic_green'>H\u01b0\u1edbng d\u1eabn: <\/span><br\/> <b> B\u01b0\u1edbc 1: <\/b> Ta t\u00e1ch: $999^2=(1000-1)^2$. <br\/> <b> B\u01b0\u1edbc 2: <\/b> Khai tri\u1ec3n theo h\u1eb1ng \u0111\u1eb3ng th\u1ee9c th\u1ee9 hai: $(a-b)^2=a^2-2ab+b^2$ \u0111\u1ec3 t\u00ednh.<br\/><span class='basic_green'>B\u00e0i gi\u1ea3i:<\/span><br\/><span class='basic_left'>Ta c\u00f3: <br\/>$999^2=(1000-1)^2=1000^2-2.1000.1+1^2=1000000-2000+1=998000+1=998001$. <span><br\/> <span class='basic_pink'> V\u1eady \u0111\u00e1p \u00e1n l\u00e0 A.<\/span>","column":2}]}],"id_ques":413},{"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/bai3/lv2/img\/1.png' \/><\/center>Gi\u00e1 tr\u1ecb c\u1ee7a bi\u1ec3u th\u1ee9c $(5a-1)^2$ t\u1ea1i $a = 2$ l\u00e0: ","select":["A. $16$","B. $81$","C. $25$","D. $100$"],"hint":" Thay $a = 2$ v\u00e0o bi\u1ec3u th\u1ee9c v\u00e0 t\u00ednh.","explain":"<span class='basic_left'>Thay $a = 2$ v\u00e0o bi\u1ec3u th\u1ee9c, ta \u0111\u01b0\u1ee3c:<br\/> $(5.2-1)^2=9^2=81$.<span><br\/> <span class='basic_pink'> V\u1eady \u0111\u00e1p \u00e1n l\u00e0 B.<\/span>","column":2}]}],"id_ques":414},{"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/bai3/lv2/img\/1.png' \/><\/center>Gi\u00e1 tr\u1ecb c\u1ee7a bi\u1ec3u th\u1ee9c $x^2-(\\dfrac{1}{y})^2$ t\u1ea1i $x = \\dfrac{-1}{2}; y = 2$ l\u00e0: ","select":["A. $0$","B. $1$","C. $2$","D. $4$"],"hint":"","explain":"<span class='basic_left'>Thay $x = \\dfrac{-1}{2}; y = 2$ v\u00e0o bi\u1ec3u th\u1ee9c \u0111\u00e3 cho, ta \u0111\u01b0\u1ee3c:<br\/> $(\\dfrac{-1}{2})^2-(\\dfrac{1}{2})^2$$=\\dfrac{1}{4}-\\dfrac{1}{4}=0$.<span><br\/> <span class='basic_pink'> V\u1eady \u0111\u00e1p \u00e1n l\u00e0 A.<\/span>","column":2}]}],"id_ques":415},{"time":24,"part":[{"title":"L\u1ef1a ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang nh\u1ea5t","title_trans":"","temp":"multiple_choice","correct":[[4]],"list":[{"point":5,"ques":"<center><img src='https://www.luyenthi123.com/file/luyenthi123/lop8/toan/daiso/bai3/lv2/img\/1.png' \/><\/center>Gi\u00e1 tr\u1ecb c\u1ee7a bi\u1ec3u th\u1ee9c $x^2y^2 -2xy+1$ t\u1ea1i $x = 1 ; y = - 1$ l\u00e0: ","select":["A. $1$","B. $2$","C. $0$","D. $4$"],"hint":"Thu g\u1ecdn bi\u1ec3u th\u1ee9c \u0111\u00e3 cho v\u1ec1 h\u1eb1ng \u0111\u1eb3ng th\u1ee9c b\u00ecnh ph\u01b0\u01a1ng c\u1ee7a m\u1ed9t hi\u1ec7u. <br\/> Thay $x = 1 ; y = - 1$ v\u00e0o bi\u1ec3u th\u1ee9c \u0111\u00e3 r\u00fat g\u1ecdn v\u00e0 t\u00ednh.","explain":"<span class='basic_left'>Ta c\u00f3: $x^2y^2 -2xy+1=(xy-1)^2$. <br\/> Thay $x = 1 ; y = - 1$ v\u00e0o bi\u1ec3u th\u1ee9c \u0111\u00e3 r\u00fat g\u1ecdn, ta \u0111\u01b0\u1ee3c:<br\/> $[1.(-1)-1]^2=(-2)^2=4$.<span><br\/> <span class='basic_pink'> V\u1eady \u0111\u00e1p \u00e1n l\u00e0 D.<\/span>","column":2}]}],"id_ques":416},{"time":24,"part":[{"title":"\u0110i\u1ec1n v\u00e0o \u00f4 tr\u1ed1ng \u0111\u1ec3 \u0111\u01b0\u1ee3c m\u1ed9t khai tri\u1ec3n \u0111\u00fang ","title_trans":"","temp":"fill_the_blank_random","correct":[[["3x"],["5"]]],"list":[{"point":5,"width":40,"type_input":"","ques":"<center><img src='https://www.luyenthi123.com/file/luyenthi123/lop8/toan/daiso/bai3/lv2/img\/1.png' \/><\/center>$9x^2+30x+25$$=(\\FormInput[40][bl_elm_true basic_elm basic_blank basic_blank_part]{}+\\FormInput[40][bl_elm_true basic_elm basic_blank basic_blank_part]{})^2$","hint":"","explain":"<span class='basic_left'><span class='basic_green'>H\u01b0\u1edbng d\u1eabn:<\/span><br\/> <b> B\u01b0\u1edbc 1: <\/b> \u0110\u01b0a VT v\u1ec1 d\u1ea1ng thu g\u1ecdn c\u1ee7a h\u1eb1ng \u0111\u1eb3ng th\u1ee9c b\u00ecnh ph\u01b0\u01a1ng c\u1ee7a m\u1ed9t t\u1ed5ng . <br\/> <b> B\u01b0\u1edbc 2: <\/b> V\u00ec VT = VP n\u00ean suy ra \u0111\u01b0\u1ee3c h\u1ea1ng t\u1eed c\u1ea7n \u0111i\u1ec1n v\u00e0o \u00f4 tr\u1ed1ng <br\/><span class='basic_green'>B\u00e0i gi\u1ea3i:<\/span><br\/>Ta c\u00f3: <br\/> $9x^2+30x+25 =(3x)^2+2.3x.5+5^2 =(3x+5)^2$. <br\/> V\u00ec VT = VP $\\Rightarrow$ $(3x+5)^2 = (3x+5)^2$ <br\/> <span class='basic_pink'>V\u1eady c\u1ea7n \u0111i\u1ec1n l\u00e0 $3x$ v\u00e0 $5$. <\/span><\/span> "}]}],"id_ques":417},{"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":[[["2a"],["5b"]]],"list":[{"point":5,"width":40,"type_input":"","ques":"<center><img src='https://www.luyenthi123.com/file/luyenthi123/lop8/toan/daiso/bai3/lv2/img\/1.png' \/><\/center>$(2a-5b)(2a+5b)$$=(\\FormInput[40][bl_elm_true basic_elm basic_blank basic_blank_part]{})^2-(\\FormInput[40][bl_elm_true basic_elm basic_blank basic_blank_part]{})^2$","hint":"","explain":"<span class='basic_left'><span class='basic_green'>H\u01b0\u1edbng d\u1eabn:<\/span><br\/> <b> B\u01b0\u1edbc 1: <\/b> \u0110\u01b0a VT v\u1ec1 d\u1ea1ng thu g\u1ecdn c\u1ee7a h\u1eb1ng \u0111\u1eb3ng th\u1ee9c hi\u1ec7u hai b\u00ecnh ph\u01b0\u01a1ng. <br\/> <b> B\u01b0\u1edbc 2: <\/b> V\u00ec VT = VT n\u00ean suy ra \u0111\u01b0\u1ee3c c\u00e1c h\u1ea1ng t\u1eed c\u1ea7n \u0111i\u1ec1n v\u00e0o \u00f4 tr\u1ed1ng. <br\/><span class='basic_green'>B\u00e0i gi\u1ea3i:<\/span><br\/>Ta c\u00f3: <br\/> $(2a-5b)(2a+5b)=(2a)^2-(5b)^2$. <br\/> V\u00ec VT = VP $\\Rightarrow$ $(2a)^2-(5b)^2 = (2a)^2-(5b)^2$ <br\/> <span class='basic_pink'>V\u1eady c\u1ea7n \u0111i\u1ec1n l\u00e0 $2a$ v\u00e0 $5b$. <\/span><\/span> "}]}],"id_ques":418},{"time":24,"part":[{"title":"\u0110i\u1ec1n v\u00e0o \u00f4 tr\u1ed1ng \u0111\u1ec3 \u0111\u01b0\u1ee3c m\u1ed9t khai tri\u1ec3n \u0111\u00fang ","title_trans":"","temp":"fill_the_blank","correct":[[["4a"],["1"]]],"list":[{"point":5,"width":40,"type_input":"","ques":"<center><img src='https://www.luyenthi123.com/file/luyenthi123/lop8/toan/daiso/bai3/lv2/img\/1.png' \/><\/center>$16a^2-8a+1$$=(\\FormInput[40][bl_elm_true basic_elm basic_blank basic_blank_part]{}-\\FormInput[40][bl_elm_true basic_elm basic_blank basic_blank_part]{})^2$","hint":"","explain":"<span class='basic_left'><span class='basic_green'>H\u01b0\u1edbng d\u1eabn:<\/span><br\/> <b> B\u01b0\u1edbc 1: <\/b> \u0110\u01b0a VT v\u1ec1 d\u1ea1ng thu g\u1ecdn c\u1ee7a h\u1eb1ng \u0111\u1eb3ng th\u1ee9c b\u00ecnh ph\u01b0\u01a1ng c\u1ee7a m\u1ed9t hi\u1ec7u. <br\/> <b> B\u01b0\u1edbc 2: <\/b> V\u00ec VT = VP n\u00ean suy ra \u0111\u01b0\u1ee3c c\u00e1c h\u1ea1ng t\u1eed c\u1ea7n \u0111i\u1ec1n v\u00e0o \u00f4 tr\u1ed1ng <br\/><span class='basic_green'>B\u00e0i gi\u1ea3i:<\/span><br\/>Ta c\u00f3: <br\/> $16a^2-8a+1=(4a)^2-2.4a.1+1^2 =(4a-1)^2$. <br\/> V\u00ec VT = VP $\\Rightarrow$ $(4a-1)^2 = (4a-1)^2$ <br\/> <span class='basic_pink'>V\u1eady c\u1ea7n \u0111i\u1ec1n l\u00e0 $4a$ v\u00e0 $1$. <\/span><\/span> "}]}],"id_ques":419},{"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":"<center><img src='https://www.luyenthi123.com/file/luyenthi123/lop8/toan/daiso/bai3/lv2/img\/1.png' \/><\/center>Khai tri\u1ec3n $9-y^2$ theo h\u1eb1ng \u0111\u1eb3ng th\u1ee9c ta \u0111\u01b0\u1ee3c:","select":["A. $3-y(3+y)$ ","B. $(3-y)(3-y)$ ","C. $(3+y)(3-y)$","D. $9-6y+y^2$"],"hint":"Khai tri\u1ec3n theo h\u1eb1ng \u0111\u1eb3ng th\u1ee9c hi\u1ec7u hai b\u00ecnh ph\u01b0\u01a1ng.","explain":"<span class='basic_left'>Ta c\u00f3:<br\/> $9-y^2=3^2-y^2=(3+y)(3-y)$<span><br\/> <span class='basic_pink'> V\u1eady \u0111\u00e1p \u00e1n l\u00e0 C.<\/span>","column":2}]}],"id_ques":420}],"lesson":{"save":0,"level":2}}