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{"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}}

Điểm của bạn.

Câu hỏi này theo dạng chọn đáp án đúng, sau khi đọc xong câu hỏi, bạn bấm vào một trong số các đáp án mà chương trình đưa ra bên dưới, sau đó bấm vào nút gửi để kiểm tra đáp án và sẵn sàng chuyển sang câu hỏi kế tiếp

Trả lời đúng trong khoảng thời gian quy định bạn sẽ được + số điểm như sau:
Trong khoảng 1 phút đầu tiên + 5 điểm
Trong khoảng 1 phút -> 2 phút + 4 điểm
Trong khoảng 2 phút -> 3 phút + 3 điểm
Trong khoảng 3 phút -> 4 phút + 2 điểm
Trong khoảng 4 phút -> 5 phút + 1 điểm

Quá 5 phút: không được cộng điểm

Tổng thời gian làm mỗi câu (không giới hạn)

Điểm của bạn.

Bấm vào đây nếu phát hiện có lỗi hoặc muốn gửi góp ý