{"segment":[{"time":24,"part":[{"title":"L\u1ef1a ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang nh\u1ea5t","title_trans":"","temp":"multiple_choice","correct":[[1]],"list":[{"point":10,"ques":"<center><img src='https://www.luyenthi123.com/file/luyenthi123/lop8/toan/daiso/bai4/lv3/img\/5.jpg' \/><\/center>Gi\u00e1 tr\u1ecb c\u1ee7a bi\u1ec3u th\u1ee9c $A=(3x+2)^3-18x(3x+2)+(x-1)^3$$-28x^3+3x(x-1)$ kh\u00f4ng ph\u1ee5 thu\u1ed9c v\u00e0o $ x$. \u0110\u00fang hay sai?","select":["\u0110\u00fang","Sai"],"hint":"R\u00fat g\u1ecdn bi\u1ec3u th\u1ee9c $A$, x\u00e9t k\u1ebft qu\u1ea3 thu \u0111\u01b0\u1ee3c c\u00f3 ch\u1ee9a $x$ hay kh\u00f4ng.<br\/> N\u1ebfu kh\u00f4ng ch\u1ee9a $x$ th\u00ec gi\u00e1 tr\u1ecb bi\u1ec3u th\u1ee9c kh\u00f4ng ph\u1ee5 thu\u1ed9c v\u00e0o $x$. ","explain":"<span class='basic_left'>Ta c\u00f3: <br\/>$ A={{(3x+2)}^{3}}-18x(3x+2)+{{(x-1)}^{3}}$$-28{{x}^{3}}+3x(x-1) $<br\/>$ =27{{x}^{3}}+54{{x}^{2}}+36x+8-54{{x}^{2}}-36x+{{x}^{3}}-3{{x}^{2}}$$+3x-1-28{{x}^{3}}+3{{x}^{2}}-3x $<br\/>$ =\\left( 27{{x}^{3}}+{{x}^{3}}-28{{x}^{3}} \\right)$$+\\left( 54{{x}^{2}}-54{{x}^{2}}-3{{x}^{2}}+3{{x}^{2}} \\right)$$+\\left( 36x-36x+3x-3x \\right)+8-1 $<br\/>$ =7 $ . <br\/>V\u1eady gi\u00e1 tr\u1ecb c\u1ee7a $A$ kh\u00f4ng ph\u1ee5 thu\u1ed9c v\u00e0o bi\u1ebfn $x$.<br\/> <span class='basic_pink'> V\u1eady \u0111\u00e1p \u00e1n l\u00e0 \u0110\u00fang.<\/span>","column":2}]}],"id_ques":471},{"time":24,"part":[{"title":"L\u1ef1a ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang nh\u1ea5t","title_trans":"","temp":"multiple_choice","correct":[[2]],"list":[{"point":10,"ques":"<center><img src='https://www.luyenthi123.com/file/luyenthi123/lop8/toan/daiso/bai4/lv3/img\/2.jpg' \/><\/center> T\u00ecm $x$, bi\u1ebft $(x+1)^3-(x-1)^3\\ge 3x+6x^2$ ","select":["A. $x\\ge -\\dfrac{3}{2}$ ","B. $x\\le \\dfrac{2}{3}$","C. $x\\ge 3$","D. $x\\le -3$"],"hint":" S\u1eed d\u1ee5ng c\u00e1c h\u1eb1ng \u0111\u1eb3ng th\u1ee9c \u0111\u00e3 h\u1ecdc \u0111\u1ec3 khai tri\u1ec3n v\u00e0 r\u00fat g\u1ecdn.","explain":"<span class='basic_left'> Ta c\u00f3: <br\/>$ {{(x+1)}^{3}}-{{(x-1)}^{3}}\\ge 3x+6{{x}^{2}} \\\\ \\Leftrightarrow {{x}^{3}}+3{{x}^{2}}+3x+1-\\left( {{x}^{3}}-3{{x}^{2}}+3x-1 \\right) \\ge 3x+6{{x}^{2}} \\\\ \\Leftrightarrow {{x}^{3}}+3{{x}^{2}}+3x+1-{{x}^{3}}+3{{x}^{2}}-3x+1 \\ge 3x+6{{x}^{2}} \\\\ \\Leftrightarrow 6{{x}^{2}}+2\\ge 3x+6{{x}^{2}} \\\\ \\Leftrightarrow 2\\ge 3x \\\\ \\Leftrightarrow x\\le \\dfrac{2}{3} $ <span><br\/> <span class='basic_pink'> V\u1eady \u0111\u00e1p \u00e1n l\u00e0 B.<\/span>","column":2}]}],"id_ques":472},{"time":24,"part":[{"title":"L\u1ef1a ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang nh\u1ea5t","title_trans":"","temp":"multiple_choice","correct":[[3]],"list":[{"point":10,"ques":"<center><img src='https://www.luyenthi123.com/file/luyenthi123/lop8/toan/daiso/bai4/lv3/img\/5.jpg' \/><\/center> Bi\u1ec3u th\u1ee9c $A=8x^3-12x^2+6x-8$ v\u1edbi $x \\ge 1$ c\u00f3 gi\u00e1 tr\u1ecb nh\u1ecf nh\u1ea5t l\u00e0: ","select":["A. $1$ ","B. $-7$","C. $-6$","D. $0$"],"hint":"","explain":"<span class='basic_left'><span class='basic_green'>H\u01b0\u1edbng d\u1eabn<\/span><br\/> <b>B\u01b0\u1edbc 1:<\/b> Vi\u1ebft $A =[f(x)]^3+a$ v\u1edbi $f(x)$ l\u00e0 bi\u1ec3u th\u1ee9c ch\u1ee9a $x, a$ l\u00e0 h\u1eb1ng s\u1ed1.<br\/> <b>B\u01b0\u1edbc 2:<\/b> T\u1eeb \u0111i\u1ec1u ki\u1ec7n $x \\ge 1$ \u0111\u1ec3 \u0111\u00e1nh gi\u00e1 t\u00ecm gi\u00e1 tr\u1ecb nh\u1ecf nh\u1ea5t c\u1ee7a $A$. <br\/> <b> B\u01b0\u1edbc 3:<\/b> GTNN c\u1ee7a $A$ \u0111\u1ea1t \u0111\u01b0\u1ee3c khi n\u00e0o. <br\/><span class='basic_green'>Gi\u1ea3i<\/span><br\/><span class='basic_left'> Ta c\u00f3: <br\/>$\\begin{align} & A=8{{x}^{3}}-12{{x}^{2}}+6x-8 \\\\ & ={{\\left( 2x-1 \\right)}^{3}}-7 \\\\ & \\text{Do} \\,\\,x\\ge 1\\Rightarrow {{\\left( 2x-1 \\right)}^{3}}\\ge {{\\left( 2.1-1 \\right)}^{3}} \\\\ & \\Rightarrow {{\\left( 2x-1 \\right)}^{3}}\\ge 1 \\\\ & A={{\\left( 2x-1 \\right)}^{3}}-7\\ge 1-7 \\\\ & \\Rightarrow A\\ge -6 \\\\ & Min\\,\\,A=-6\\Leftrightarrow x=1 \\\\ \\end{align}$ <br\/> <span class='basic_pink'> V\u1eady \u0111\u00e1p \u00e1n l\u00e0 C.<\/span>","column":2}]}],"id_ques":473},{"time":24,"part":[{"title":"L\u1ef1a ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang nh\u1ea5t","title_trans":"","temp":"multiple_choice","correct":[[1]],"list":[{"point":10,"ques":"<center><img src='https://www.luyenthi123.com/file/luyenthi123/lop8/toan/daiso/bai4/lv3/img\/5.jpg' \/><\/center>Cho $x =a-1$. Khi \u0111\u00f3 $x^3+3ax-a^3+1$ b\u1eb1ng: ","select":["A. $0$ ","B. $1$","C. $-2$","D. $3$"],"hint":"Thay $x=a-1$ v\u00e0o bi\u1ec3u th\u1ee9c $x^3+3ax-a^3+1$ v\u00e0 r\u00fat g\u1ecdn.","explain":"<span class='basic_left'>Thay $x = a \u2013 1$ v\u00e0o bi\u1ec3u th\u1ee9c ta \u0111\u01b0\u1ee3c: <br\/> $ {{x}^{3}}+3ax-{{a}^{3}}+1 $<br\/>$ ={{\\left( a-1 \\right)}^{3}}+3a\\left( a-1 \\right)$$-{{a}^{3}}+1 $<br\/>$ ={{a}^{3}}-3{{a}^{2}}+3a-1+3{{a}^{2}}-3a$$-{{a}^{3}}+1 $<br\/>$ =0 $ <br\/> <span class='basic_pink'> V\u1eady \u0111\u00e1p \u00e1n l\u00e0 A.<\/span>","column":2}]}],"id_ques":474},{"time":24,"part":[{"title":"\u0110i\u1ec1n k\u1ebft qu\u1ea3 v\u00e0o \u00f4 tr\u1ed1ng ","title_trans":"","temp":"fill_the_blank_random","correct":[[["0"],["-2"]]],"list":[{"point":10,"width":40,"type_input":"","ques":"<center><img src='https://www.luyenthi123.com/file/luyenthi123/lop8/toan/daiso/bai4/lv3/img\/4.jpg' \/><\/center>Bi\u1ebft $x^6+9x^5+27x^4+27x^3=x^3$, gi\u00e1 tr\u1ecb c\u1ee7a $x$ l\u00e0 _input_ ho\u1eb7c _input_","hint":"S\u1eed d\u1ee5ng h\u1eb3ng \u0111\u1eb3ng th\u1ee9c l\u1eadp ph\u01b0\u01a1ng c\u1ee7a m\u1ed9t t\u1ed5ng \u0111\u1ec3 bi\u1ebfn \u0111\u1ed5i v\u1ebf tr\u00e1i <br\/> N\u1ebfu $a^3=b^3$ th\u00ec $a = b$<br\/> N\u1ebfu $a.b = 0$ th\u00ec ho\u1eb7c $a = 0$ ho\u1eb7c $b = 0$","explain":"<span class='basic_left'>Ta c\u00f3: <br\/>$ {{x}^{6}}+9{{x}^{5}}+27{{x}^{4}}+27{{x}^{3}}={{x}^{3}} \\\\ \\Leftrightarrow {{\\left( {{x}^{2}}+3x \\right)}^{3}}={{x}^{3}} \\\\ \\Leftrightarrow {{x}^{2}}+3x=x \\\\ \\Leftrightarrow {{x}^{2}}+2x=0 \\\\ \\Leftrightarrow x\\left( x+2 \\right) =0 \\\\ \\Leftrightarrow \\left[ \\begin{aligned} & x=0 \\\\ & x+2=0 \\\\ \\end{aligned} \\right.\\\\ \\Leftrightarrow \\left[ \\begin{aligned} & x=0 \\\\ & x=-2 \\\\ \\end{aligned} \\right. $ <br\/> <span class='basic_pink'> V\u1eady s\u1ed1 c\u1ea7n \u0111i\u1ec1n v\u00e0o \u00f4 tr\u1ed1ng l\u00e0 $0$ v\u00e0 $-2$ <\/span><\/span> "}]}],"id_ques":475},{"time":24,"part":[{"title":"\u0110i\u1ec1n k\u1ebft qu\u1ea3 v\u00e0o \u00f4 tr\u1ed1ng ","title_trans":"","temp":"fill_the_blank","correct":[[["-3375"]]],"list":[{"point":10,"width":40,"type_input":"","ques":"<center><img src='https://www.luyenthi123.com/file/luyenthi123/lop8/toan/daiso/bai4/lv3/img\/2.jpg' \/><\/center> Gi\u00e1 tr\u1ecb c\u1ee7a bi\u1ec3u th\u1ee9c $1-3y^4+3y^8-y^{12}$ v\u1edbi $y = - 2$ l\u00e0 _input_","hint":"R\u00fat g\u1ecdn: $1-3y^4+3y^8-y^{12}=(1-y^4)^3$.<br\/> Thay $y = - 2$ v\u00e0o bi\u1ec3u th\u1ee9c r\u00fat g\u1ecdn r\u1ed3i t\u00ednh. ","explain":"<span class='basic_left'> Ta c\u00f3: $1-3y^4+3y^8-y^{12}=(1-y^4)^3$<br\/> Thay $y = - 2$ v\u00e0o bi\u1ec3u th\u1ee9c sau khi r\u00fat g\u1ecdn, ta \u0111\u01b0\u1ee3c: <br\/>${{\\left[ 1-{{\\left( -2 \\right)}^{4}} \\right]}^{3}}={{\\left[ 1-16 \\right]}^{3}}={{\\left( -15 \\right)}^{3}}=-3375$ <br\/> <span class='basic_pink'> V\u1eady s\u1ed1 c\u1ea7n \u0111i\u1ec1n v\u00e0o \u00f4 tr\u1ed1ng l\u00e0 $-3375$ <\/span><\/span> "}]}],"id_ques":476},{"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":10,"width":40,"type_input":"","ques":"<center><img src='https://www.luyenthi123.com/file/luyenthi123/lop8/toan/daiso/bai4/lv3/img\/5.jpg' \/><\/center>${{\\left( {{y}^{3}}-1 \\right)}^{3}}$$={{y}^{9}}\\FormInput[40][bl_elm_true basic_elm basic_blank basic_blank_part]{}3{{y}^{6}}\\FormInput[40][bl_elm_true basic_elm basic_blank basic_blank_part]{}3{{y}^{3}}\\FormInput[40][bl_elm_true basic_elm basic_blank basic_blank_part]{}1$ ","hint":"Ta khai tri\u1ec3n ${{\\left( {{y}^{3}}-1 \\right)}^{3}}$ theo h\u1eb1ng \u0111\u1eb3ng th\u1ee9c l\u1eadp ph\u01b0\u01a1ng c\u1ee7a m\u1ed9t hi\u1ec7u ${{\\left( a-b \\right)}^{3}}$$={{a}^{3}}-3{{a}^{2}}b+3a{{b}^{2}}-{{b}^{3}}$ , t\u1eeb \u0111\u00f3 t\u00ecm ra c\u00e1c d\u1ea5u c\u1ea7n \u0111i\u1ec1n v\u00e0o \u00f4 tr\u1ed1ng","explain":"<span class='basic_left'>Ta c\u00f3: <br\/>${{\\left( {{y}^{3}}-1 \\right)}^{3}}$$={{\\left( {{y}^{3}} \\right)}^{3}}-3.{{\\left( {{y}^{3}} \\right)}^{2}}.1+3.{{y}^{3}}{{.1}^{2}}-{{1}^{3}}$$={{y}^{9}}-3{{y}^{6}}+3{{y}^{3}}-1$. <br\/> <span class='basic_pink'> V\u1eady d\u1ea5u c\u1ea7n v\u00e0o \u00f4 tr\u1ed1ng l\u1ea7n l\u01b0\u1ee3t c\u00e1c d\u1ea5u $-, +$ v\u00e0 $-$ <\/span><\/span> "}]}],"id_ques":477},{"time":24,"part":[{"title":"\u0110i\u1ec1n d\u1ea5u $+$ ho\u1eb7c $-$ v\u00e0o \u00f4 tr\u1ed1ng \u0111\u1ec3 \u0111\u01b0\u1ee3c m\u1ed9t khai tri\u1ec3n \u0111\u00fang ","title_trans":"","temp":"fill_the_blank","correct":[[["+"],["-"],["-"]]],"list":[{"point":10,"width":40,"type_input":"","ques":"<center><img src='https://www.luyenthi123.com/file/luyenthi123/lop8/toan/daiso/bai4/lv3/img\/5.jpg' \/><\/center>${{\\left( 3y-{{y}^{2}} \\right)}^{3}}$$=27{{y}^{3}}\\FormInput[40][bl_elm_true basic_elm basic_blank basic_blank_part]{}9{{y}^{5}}\\FormInput[40][bl_elm_true basic_elm basic_blank basic_blank_part]{}27{{y}^{4}}\\FormInput[40][bl_elm_true basic_elm basic_blank basic_blank_part]{}{{y}^{6}}$ ","hint":"Ta khai tri\u1ec3n ${{\\left( 3y-{{y}^{2}} \\right)}^{3}}$ theo h\u1eb1ng \u0111\u1eb3ng th\u1ee9c l\u1eadp ph\u01b0\u01a1ng c\u1ee7a m\u1ed9t hi\u1ec7u ${{\\left( a-b \\right)}^{3}}={{a}^{3}}-3{{a}^{2}}b+3a{{b}^{2}}-{{b}^{3}}$ , t\u1eeb \u0111\u00f3 t\u00ecm ra c\u00e1c d\u1ea5u c\u1ea7n \u0111i\u1ec1n v\u00e0o \u00f4 tr\u1ed1ng","explain":"<span class='basic_left'>Ta c\u00f3: <br\/>$ {{\\left( 3y-{{y}^{2}} \\right)}^{3}}$$={{\\left( 3y \\right)}^{3}}-3.{{\\left( 3y \\right)}^{2}}.{{y}^{2}}+3.3y.{{\\left( {{y}^{2}} \\right)}^{2}}$$-{{\\left( {{y}^{2}} \\right)}^{3}} $<br\/>$ =27{{y}^{3}}-27{{y}^{4}}+9{{y}^{5}}-{{y}^{6}} $<br\/>$ =27{{y}^{3}}+9{{y}^{5}}-27{{y}^{4}}-{{y}^{6}} $ <br\/> <span class='basic_pink'> V\u1eady c\u00e1c d\u1ea5u c\u1ea7n \u0111i\u1ec1n v\u00e0o \u00f4 tr\u1ed1ng l\u1ea7n l\u01b0\u1ee3t l\u00e0 d\u1ea5u $+, -$ v\u00e0 $-$ <\/span><\/span> "}]}],"id_ques":478},{"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":[[["-192"],["192"],["-64"]]],"list":[{"point":10,"width":40,"type_input":"","ques":"<center><img src='https://www.luyenthi123.com/file/luyenthi123/lop8/toan/daiso/bai4/lv3/img\/2.jpg' \/><\/center>${{\\left( 4xy-4x \\right)}^{3}}$$=64{{x}^{3}}{{y}^{3}}+\\FormInput[40][bl_elm_true basic_elm basic_blank basic_blank_part]{}{{x}^{3}}{{y}^{2}}+\\FormInput[40][bl_elm_true basic_elm basic_blank basic_blank_part]{}{{x}^{3}}y+\\FormInput[40][bl_elm_true basic_elm basic_blank basic_blank_part]{}{{x}^{3}}$ ","hint":"Khai tri\u1ec3n v\u1ebf tr\u00e1i theo h\u1eb1ng \u0111\u1eb3ng th\u1ee9c l\u1eadp ph\u01b0\u01a1ng c\u1ee7a m\u1ed9t hi\u1ec7u. T\u1eeb \u0111\u00f3 x\u00e1c \u0111\u1ecbnh s\u1ed1 c\u1ea7n \u0111i\u1ec1n v\u00e0o \u00f4 tr\u1ed1ng.","explain":"<span class='basic_left'>Ta c\u00f3: <br\/> ${{\\left( 4xy-4x \\right)}^{3}}={{\\left( 4xy \\right)}^{3}}-3.{{\\left( 4xy \\right)}^{2}}.4x+3.4xy.{{\\left( 4x \\right)}^{2}}-{{\\left( 4x \\right)}^{3}}=64{{x}^{3}}{{y}^{3}}-192{{x}^{3}}{{y}^{2}}+192{{x}^{3}}y-64{{x}^{3}}$.<br\/> <span class='basic_pink'>V\u1eady c\u00e1c s\u1ed1 c\u1ea7n \u0111i\u1ec1n l\u00e0 $-192 ; 192$ v\u00e0 $-64 $. <\/span><\/span> "}]}],"id_ques":479},{"time":24,"part":[{"title":"L\u1ef1a ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang nh\u1ea5t","title_trans":"","temp":"multiple_choice","correct":[[3]],"list":[{"point":10,"ques":"<center><img src='https://www.luyenthi123.com/file/luyenthi123/lop8/toan/daiso/bai4/lv3/img\/3.jpg' \/><\/center>Khai tri\u1ec3n $(a+b+c)^3$ theo h\u1eb1ng \u0111\u1eb3ng th\u1ee9c ta \u0111\u01b0\u1ee3c:","select":["A. $a^3+b^3+c^3+3a^2b+3bc^2$ ","B. $a^3+3a^2bc+3ab^2c+3abc^2+b^3+c^3$ ","C. $a^3+3a^2(b+c)+3a(b+c)^2+(b+c)^3$","D. $a^3+b^3+c^3$"],"hint":"","explain":"<span class='basic_left'>Ta c\u00f3:<br\/> $(a+b+c)^3$ <br\/> $=[a+(b+c)]^3$<br\/> $=a^3+3a^2(b+c)+3a(b+c)^2+(b+c)^3$ <span><br\/> <span class='basic_pink'> V\u1eady \u0111\u00e1p \u00e1n l\u00e0 C.<\/span>","column":2}]}],"id_ques":480}],"lesson":{"save":0,"level":3}}