{"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/lv1/img\/1.png' \/><\/center>Bi\u1ec3u th\u1ee9c $A=x^2-8x+20$ lu\u00f4n \u00e2m v\u1edbi m\u1ecdi $x$. \u0110\u00fang hay sai?","select":["\u0110\u00fang","Sai"],"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> Sau \u0111\u00f3 \u0111\u00e1nh gi\u00e1: $A=[f(x)]^2+a$ l\u00e0 s\u1ed1 d\u01b0\u01a1ng hay \u00e2m \u0111\u1ec3 k\u1ebft lu\u1eadn b\u00e0i to\u00e1n.<br\/> <span class='basic_green'>Gi\u1ea3i<\/span><br\/><span class='basic_left'>Ta c\u00f3: <br\/> $A=x^2-8x+20$<br\/>$=(x^2-2.x.4+4^2)+4$<br\/>$=(x-4)^2+4\\ge 4 > 0$ v\u1edbi m\u1ecdi $x$<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 Sai.<\/span>","column":2}]}],"id_ques":381},{"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/lv1/img\/1.png' \/><\/center>Bi\u1ec3u th\u1ee9c $A=4{{x}^{2}}+12xy+9{{y}^{2}}+5$ lu\u00f4n d\u01b0\u01a1ng v\u1edbi m\u1ecdi $x, y$. \u0110\u00fang hay sai? ","select":["\u0110\u00fang","Sai"],"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: $A=[f(x,y)]^2+a$ v\u1edbi $a$ l\u00e0 h\u1eb1ng s\u1ed1, $f(x,y)$ l\u00e0 bi\u1ec3u th\u1ee9c ch\u1ee9a bi\u1ebfn $x, y$ <br\/> <b>B\u01b0\u1edbc 2:<\/b> \u0110\u00e1nh gi\u00e1: $A=[f(x,y)]^2+a\\ge a$<br\/><b>B\u01b0\u1edbc 3:<\/b> Xem $a$ l\u00e0 s\u1ed1 d\u01b0\u01a1ng hay \u00e2m \u0111\u1ec3 k\u1ebft lu\u1eadn b\u00e0i to\u00e1n.<br\/> <span class='basic_green'>B\u00e0i gi\u1ea3i:<\/span><br\/><span class='basic_left'>Ta c\u00f3: <br\/>$\\begin{aligned} & A=4{{x}^{2}}+12xy+9{{y}^{2}}+5 \\\\ & ={{\\left( 2x \\right)}^{2}}+2.2x.3y+{{\\left( 3y \\right)}^{2}}+5 \\\\ & ={{\\left( 2x+3y \\right)}^{2}}+5 \\\\ \\end{aligned}$ <br\/> Do ${{\\left( 2x+3y \\right)}^{2}}\\ge 0$ <br\/> $\\Rightarrow {{\\left( 2x+3y \\right)}^{2}}+5 \\ge 5 > 0$ v\u1edbi m\u1ecdi $x$. <br\/>V\u1eady $A$ lu\u00f4n d\u01b0\u01a1ng v\u1edbi m\u1ecdi $x, y$.<br\/> <span class='basic_pink'> V\u1eady \u0111\u00e1p \u00e1n l\u00e0 \u0110\u00fang.<\/span>","column":2}]}],"id_ques":382},{"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 $B=-y^2-2y-2$ 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 $B$ v\u1ec1 d\u1ea1ng: $B=b-[f(y)]^2$ v\u1edbi $b$ l\u00e0 h\u1eb1ng s\u1ed1, $f(y)$ l\u00e0 bi\u1ec3u th\u1ee9c ch\u1ee9a bi\u1ebfn $y$. <br\/><b> B\u01b0\u1edbc 2:<\/b> \u0110\u00e1nh gi\u00e1: $B=b-[f(y)]^2\\le b.$<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 nh\u1eadn th\u1ea5y:<br\/> $B=-y^2-2y-2$<br\/>$=-(y^2+2.y.1+1+1)$<br\/>$=-(y+1)^2-1$.<br\/> V\u00ec $(y + 1)^2 \\geq 0$ v\u1edbi $\\forall x$ $\\Rightarrow$ $-(y + 1)^2 \\leq 0$ v\u1edbi $\\forall x$ <br\/> $\\Rightarrow$ $-(y+1)^2-1\\le -1$ v\u1edbi m\u1ecdi $x$<br\/> Gi\u00e1 tr\u1ecb l\u1edbn nh\u1ea5t c\u1ee7a $B$ l\u00e0 $-1$.<br\/> \u0110\u1ea1t \u0111\u01b0\u1ee3c khi $y+1=0 \\Leftrightarrow y = -1.$<br\/> <span class='basic_pink'> V\u1eady c\u1ea7n \u0111i\u1ec1n v\u00e0o \u00f4 tr\u1ed1ng l\u00e0 $-1$.<\/span>"}]}],"id_ques":383},{"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 $B=-x^2-1$ l\u00e0 _input_","hint":"\u0110\u00e1nh gi\u00e1 xem $B$ lu\u00f4n nh\u1ecf h\u01a1n ho\u1eb7c b\u1eb1ng s\u1ed1 n\u00e0o, \u0111\u00f3 ch\u00ednh l\u00e0 GTLN c\u1ee7a $B$","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 $B \\le a$ <br\/> <b> B\u01b0\u1edbc 2: <\/b> Suy ra GTLN c\u1ee7a $B$ l\u00e0 $a$, v\u00e0 GTLN \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\/> $x^2\\ge 0\\Rightarrow -x^2\\le 0 $ $\\Rightarrow -x^2-1\\le -1$ v\u1edbi m\u1ecdi $x$<br\/> Gi\u00e1 tr\u1ecb l\u1edbn nh\u1ea5t c\u1ee7a B l\u00e0 $-1$.<br\/> \u0110\u1ea1t \u0111\u01b0\u1ee3c khi: $ x^2=0 \\Leftrightarrow x = 0$. <br\/> <span class='basic_pink'> V\u1eady c\u1ea7n \u0111i\u1ec1n v\u00e0o \u00f4 tr\u1ed1ng l\u00e0 $-1$. <\/span>"}]}],"id_ques":384},{"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":[[["3"]]],"list":[{"point":5,"width":40,"content":"","type_input":"","ques":"Gi\u00e1 tr\u1ecb nh\u1ecf nh\u1ea5t c\u1ee7a $A=4y^2-4y+4$ 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> Bi\u1ebfn \u0111\u1ed5i bi\u1ec3u th\u1ee9c $A$ v\u1ec1 d\u1ea1ng: $A=[f(y)]^2+a$ v\u1edbi $a$ l\u00e0 h\u1eb1ng s\u1ed1, $f(y)$ l\u00e0 bi\u1ec3u th\u1ee9c ch\u1ee9a bi\u1ebfn $y$. <br\/> <b>B\u01b0\u1edbc 2:<\/b> \u0110\u00e1nh gi\u00e1: $A=[f(y)]^2+a\\ge a$<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\/> $A=4y^2-4y+4$<br\/>$=(2y)^2-2.2y.1+1+3$<br\/>$=(2y-1)^2+3$.<br\/> Do $(2y-1)^2\\ge 0\\Leftrightarrow (2y-1)^2+3\\ge 3$ v\u1edbi m\u1ecdi $x$ <br\/>Gi\u00e1 tr\u1ecb nh\u1ecf nh\u1ea5t c\u1ee7a $A$ l\u00e0 $3$.<br\/> \u0110\u1ea1t \u0111\u01b0\u1ee3c khi $2y-1=0 \\Leftrightarrow y = \\dfrac{1}{2}.$<br\/> <span class='basic_pink'> V\u1eady c\u1ea7n \u0111i\u1ec1n v\u00e0o \u00f4 tr\u1ed1ng l\u00e0 $3$.<\/span>"}]}],"id_ques":385},{"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 $A=x^2-1$ 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 $x^2\\ge 0$ <br\/> <b> B\u01b0\u1edbc 2: <\/b> $x^2+a\\ge a.$ <br\/> <span class='basic_green'>B\u00e0i gi\u1ea3i:<\/span><br\/>Ta nh\u1eadn th\u1ea5y:<br\/> $x^2\\ge 0\\Leftrightarrow x^2-1\\ge -1$ v\u1edbi m\u1ecdi $x$<br\/> Gi\u00e1 tr\u1ecb nh\u1ecf nh\u1ea5t c\u1ee7a $A$ l\u00e0 $-1$.<br\/> \u0110\u1ea1t \u0111\u01b0\u1ee3c khi: $ x^2=0 \\Leftrightarrow x = 0$. <br\/> <span class='basic_pink'> V\u1eady c\u1ea7n \u0111i\u1ec1n v\u00e0o \u00f4 tr\u1ed1ng l\u00e0 $-1$. <\/span>"}]}],"id_ques":386},{"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 $4x^2-1=0$, gi\u00e1 tr\u1ecb c\u1ee7a $x$ l\u00e0:","select":["A. $\\pm 2$","B. $\\pm 4$","C. $\\pm \\dfrac{1}{4}$","D. $\\pm \\dfrac{1}{2}$"],"hint":"Khai tri\u1ec3n VT theo h\u1eb1ng \u0111\u1eb3ng th\u1ee9c: $a^2-b^2=(a+b)(a-b)$.<br\/> N\u1ebfu $a.b = 0$ th\u00ec $a = 0$ ho\u1eb7c $b = 0$.","explain":"<span class='basic_left'> Ta c\u00f3: <br\/> $ 4{{x}^{2}}-1 =0 $<br\/>$ \\Leftrightarrow \\left( 2x-1 \\right)\\left( 2x+1 \\right) =0 $<br\/>$ \\Leftrightarrow \\left[ \\begin{aligned} & 2x-1=0 \\\\ & 2x+1=0 \\\\ \\end{aligned} \\right.$$\\Leftrightarrow \\left[ \\begin{aligned} & x=\\dfrac{1}{2} \\\\ & x=\\dfrac{-1}{2} \\\\ \\end{aligned} \\right. $ <br\/><span class='basic_pink'> V\u1eady \u0111\u00e1p \u00e1n \u0111\u00fang l\u00e0 D.<\/span><\/span>","column":2}]}],"id_ques":387},{"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":"Bi\u1ebft $y^2-6y+9=0$, gi\u00e1 tr\u1ecb c\u1ee7a $y$ l\u00e0:","select":["A. $9$","B. $4$","C. $3$","D. $2$"],"hint":"Thu g\u1ecdn v\u1ebf tr\u00e1i theo h\u1eb1ng \u0111\u1eb3ng th\u1ee9c b\u00ecnh ph\u01b0\u01a1ng c\u1ee7a m\u1ed9t hi\u1ec7u r\u1ed3i t\u00ecm $y$","explain":"<span class='basic_left'> Ta c\u00f3: <br\/> $\\begin{align} & y^2-6y+9 =0\\\\ &\\Leftrightarrow (y-3)^2=0\\\\ & \\Leftrightarrow y-3 =0\\\\ & \\Leftrightarrow y=3\\\\ \\end{align}$ <br\/><span class='basic_pink'> V\u1eady \u0111\u00e1p \u00e1n \u0111\u00fang l\u00e0 C.<\/span><\/span>","column":2}]}],"id_ques":388},{"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 $x^2-2x+1=0$, gi\u00e1 tr\u1ecb c\u1ee7a $x$ l\u00e0:","select":["A. $1$","B. $-1$","C. $2$","D. $-2$"],"hint":"Thu g\u1ecdn VT theo h\u1eb1ng \u0111\u1eb3ng th\u1ee9c b\u00ecnh ph\u01b0\u01a1ng c\u1ee7a m\u1ed9t hi\u1ec7u r\u1ed3i t\u00ecm $x$.","explain":"<span class='basic_left'>Ta c\u00f3: <br\/> $\\begin{align} & x^2-2x+1=0\\\\ &\\Leftrightarrow (x-1)^2=0\\\\ &\\Leftrightarrow x-1 =0\\\\ & \\Leftrightarrow x =1\\\\ \\end{align}$ <br\/><span class='basic_pink'> V\u1eady \u0111\u00e1p \u00e1n \u0111\u00fang l\u00e0 A.<\/span><\/span>","column":2}]}],"id_ques":389},{"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/lv1/img\/1.png' \/><\/center>Gi\u00e1 tr\u1ecb c\u1ee7a bi\u1ec3u th\u1ee9c $y^2 +6y+9$ t\u1ea1i $y = -1$ l\u00e0: ","select":["A. $4$","B. $1$","C. $9$","D. $18$"],"hint":"R\u00fat g\u1ecdn bi\u1ec3u th\u1ee9c r\u1ed3i thay $y = -1$ v\u00e0o bi\u1ec3u th\u1ee9c \u0111\u00e3 r\u00fat g\u1ecdn v\u00e0 t\u00ednh.","explain":"<span class='basic_left'><span class='basic_green'>H\u01b0\u1edbng d\u1eabn<\/span><br\/> <b>B\u01b0\u1edbc 1:<\/b> R\u00fat g\u1ecdn bi\u1ec3u th\u1ee9c b\u1eb1ng c\u00e1ch \u00e1p d\u1ee5ng h\u1eb1ng \u0111\u1eb3ng th\u1ee9c b\u00ecnh ph\u01b0\u01a1ng c\u1ee7a m\u1ed9t t\u1ed5ng. <br\/> <b>B\u01b0\u1edbc 2:<\/b> Thay $y = -1$ v\u00e0o bi\u1ec3u th\u1ee9c \u0111\u00e3 r\u00fat g\u1ecdn v\u00e0 t\u00ednh.<br\/><span class='basic_green'>Gi\u1ea3i<\/span><br\/><span class='basic_left'>Ta c\u00f3: <br\/>$y^2+6y+9=y^2+2.y.3+3^2 =(y+3)^2$. <br\/> Thay $y = -1$ v\u00e0o bi\u1ec3u th\u1ee9c \u0111\u00e3 r\u00fat g\u1ecdn, ta \u0111\u01b0\u1ee3c:<br\/> $(-1+3)^2=2^2=4$.<span><br\/> <span class='basic_pink'> V\u1eady \u0111\u00e1p \u00e1n l\u00e0 A.<\/span>","column":2}]}],"id_ques":390},{"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/lv1/img\/1.png' \/><\/center>Gi\u00e1 tr\u1ecb c\u1ee7a bi\u1ec3u th\u1ee9c $4x^2 -4x+1$ t\u1ea1i $x = 1$ l\u00e0: ","select":["A. $4$","B. $1$","C. $9$","D.$ 6$"],"hint":"R\u00fat g\u1ecdn bi\u1ec3u th\u1ee9c r\u1ed3i thay $x = 1$ v\u00e0o bi\u1ec3u th\u1ee9c \u0111\u00e3 r\u00fat g\u1ecdn v\u00e0 t\u00ednh.","explain":"<span class='basic_left'><span class='basic_green'>H\u01b0\u1edbng d\u1eabn<\/span><br\/> <b>B\u01b0\u1edbc 1:<\/b> R\u00fat g\u1ecdn bi\u1ec3u th\u1ee9c b\u1eb1ng c\u00e1ch s\u1eed d\u1ee5ng h\u1eb1ng \u0111\u1eb3ng th\u1ee9c b\u00ecnh ph\u01b0\u01a1ng c\u1ee7a m\u1ed9t hi\u1ec7u. <br\/> <b>B\u01b0\u1edbc 2:<\/b> Thay $x = 1$ v\u00e0o bi\u1ec3u th\u1ee9c \u0111\u00e3 r\u00fat g\u1ecdn v\u00e0 t\u00ednh.<br\/><span class='basic_green'>Gi\u1ea3i<\/span><br\/><span class='basic_left'>Ta c\u00f3: <br\/>$4x^2-4x+1 = (2x)^2-2.2x.1+1^2 =(2x-1)^2.$ <br\/> Thay $x = 1$ v\u00e0o bi\u1ec3u th\u1ee9c \u0111\u00e3 r\u00fat g\u1ecdn, ta \u0111\u01b0\u1ee3c:<br\/> $(2.1-1)^2=1^2=1.$<span><br\/> <span class='basic_pink'> V\u1eady \u0111\u00e1p \u00e1n l\u00e0 B.<\/span>","column":2}]}],"id_ques":391},{"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/lv1/img\/1.png' \/><\/center>T\u00ednh nhanh (kh\u00f4ng s\u1eed d\u1ee5ng m\u00e1y t\u00ednh): $301^2$. <br\/> \u0110\u00e1p \u00e1n l\u00e0:","select":["A. $89401$","B. $602$","C. $90601$","D. $90000$"],"hint":"Ta t\u00e1ch: $301^2=(300+1)^2$.<br\/> 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.","explain":"<span class='basic_left'> Ta c\u00f3: <br\/>$301^2=(300+1)^2$<br\/>$=300^2+2.300.1+1^2$<br\/>$=90000+600+1=90601.$ <span><br\/> <span class='basic_pink'> V\u1eady \u0111\u00e1p \u00e1n l\u00e0 C.<\/span>","column":2}]}],"id_ques":392},{"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/lv1/img\/1.png' \/><\/center>T\u00ednh nhanh (kh\u00f4ng s\u1eed d\u1ee5ng m\u00e1y t\u00ednh): $19^2$. <br\/> \u0110\u00e1p \u00e1n l\u00e0:","select":["A. $361$","B. $400$","C. $461$","D. $341$"],"hint":"Ta t\u00e1ch: $19^2=(20-1)^2$.<br\/> 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.","explain":"<span class='basic_left'>Ta c\u00f3: <br\/>$19^2=(20-1)^2 =20^2-2.20.1+1^2=400-40+1 =360+1=361$. <span><br\/> <span class='basic_pink'> V\u1eady \u0111\u00e1p \u00e1n l\u00e0 A.<\/span>","column":2}]}],"id_ques":393},{"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/lv1/img\/1.png' \/><\/center>T\u00ednh nhanh (kh\u00f4ng s\u1eed d\u1ee5ng m\u00e1y t\u00ednh): $47.53$. <br\/> \u0110\u00e1p \u00e1n l\u00e0:","select":["A. $2481$","B. $2461$","C. $2451$","D. $2491$"],"hint":"Ta t\u00e1ch: $47=50-3$; $53=50+3$.<br\/>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.","explain":"<span class='basic_left'>Ta c\u00f3: <br\/>$47.53=(50-3)(50+3)$<br\/>$=50^2-3^2=2500-9=2491$. <span><br\/> <span class='basic_pink'> V\u1eady \u0111\u00e1p \u00e1n l\u00e0 D.<\/span>","column":2}]}],"id_ques":394},{"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/lv1/img\/1.png' \/><\/center>T\u00ednh nhanh: $101^2$. <br\/> \u0110\u00e1p \u00e1n l\u00e0:","select":["A. $10201$","B. $100000$ ","C. $20202$","D. $11111$"],"hint":"Ta t\u00e1ch: $101^2=(100+1)^2$.<br\/> 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.","explain":"<span class='basic_left'>Ta c\u00f3: <br\/>$101^2=(100+1)^2 =100^2+2.100.1+1^2 =10000+200+1=10201$. <span><br\/> <span class='basic_pink'> V\u1eady \u0111\u00e1p \u00e1n l\u00e0 A.<\/span>","column":2}]}],"id_ques":395},{"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":[[["2"]]],"list":[{"point":5,"width":40,"type_input":"","ques":"<center><img src='https://www.luyenthi123.com/file/luyenthi123/lop8/toan/daiso/bai3/lv1/img\/1.png' \/><\/center>$a^2+\\FormInput[40][bl_elm_true basic_elm basic_blank basic_blank_part]{}ab+b^2=(a+b)^2$","hint":"Khai tri\u1ec3n V\u1ebf ph\u1ea3i theo h\u1eb1ng \u0111\u1eb3ng th\u1ee9c: $(a+b)^2=a^2+2ab+b^2$ r\u1ed3i t\u1eeb \u0111\u00f3 t\u00ecm h\u1ec7 s\u1ed1 t\u01b0\u01a1ng \u1ee9ng v\u1edbi $a$, $b$ \u1edf v\u1ebf tr\u00e1i ","explain":"<span class='basic_left'>Ta c\u00f3: <br\/> $(a+b)^2=a^2+2.a.b+b^2$$=a^2+2ab+b^2$.<br\/> <span class='basic_pink'>V\u1eady \u0111\u00e1p \u00e1n c\u1ea7n \u0111i\u1ec1n l\u00e0 $2$. <\/span><\/span> "}]}],"id_ques":396},{"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":[[["2x"],["1"]]],"list":[{"point":5,"width":40,"type_input":"","ques":"<center><img src='https://www.luyenthi123.com/file/luyenthi123/lop8/toan/daiso/bai3/lv1/img\/1.png' \/><\/center>$(2x-1)(2x+1)$$=(\\FormInput[40][bl_elm_true basic_elm basic_blank basic_blank_part]{})^2-\\FormInput[40][bl_elm_true basic_elm basic_blank basic_blank_part]{}^2$","hint":"Khai tri\u1ec3n VT theo h\u1eb1ng \u0111\u1eb3ng th\u1ee9c $a^2\u2212b^2=(a\u2212b)(a+b)$, t\u1eeb \u0111\u00f3 suy ra \u00f4 tr\u1ed1ng c\u1ea7n \u0111i\u1ec1n.","explain":"<span class='basic_left'>Ta c\u00f3: <br\/> $(2x-1)(2x+1)=(2x)^2-1^2$.<br\/> <span class='basic_pink'>V\u1eady \u0111\u00e1p \u00e1n c\u1ea7n \u0111i\u1ec1n l\u00e0 $2x$ v\u00e0 $1$. <\/span><\/span> "}]}],"id_ques":397},{"time":24,"part":[{"title":"\u0110i\u1ec1n v\u00e0o \u00f4 tr\u1ed1ng \u0111\u1ec3 \u0111\u01b0\u1ee3c m\u1ed9t khai tri\u1ec3n \u0111\u00fang ","title_trans":"","temp":"fill_the_blank","correct":[[["x"],["2"]]],"list":[{"point":5,"width":40,"type_input":"","ques":"<center><img src='https://www.luyenthi123.com/file/luyenthi123/lop8/toan/daiso/bai3/lv1/img\/1.png' \/><\/center>$x^2-4x+4$$=(\\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":"Theo h\u1eb1ng \u0111\u1eb3ng th\u1ee9c th\u1ee9 hai: $(a-b)^2=a^2-2ab+b^2$.<br\/> T\u1eeb \u0111\u00f3 t\u00ecm ng\u01b0\u1ee3c l\u1ea1i $a$ v\u00e0 $b$.","explain":"<span class='basic_left'>Ta c\u00f3: <br\/> $x^2-4x+4=x^2-2.x.2+2^2=(x-2)^2$.<br\/> <span class='basic_pink'>V\u1eady \u0111\u00e1p \u00e1n c\u1ea7n \u0111i\u1ec1n l\u00e0 $x$ v\u00e0 $2$. <\/span><\/span> "}]}],"id_ques":398},{"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/lv1/img\/1.png' \/><\/center>Khai tri\u1ec3n $(1-x)^2$ theo h\u1eb1ng \u0111\u1eb3ng th\u1ee9c ta \u0111\u01b0\u1ee3c:","select":["A. $1-x-x^2$ ","B. $1-2x+x^2$ ","C. $1+2x+x^2$","D. $1+x+x^2$"],"hint":"Khai tri\u1ec3n theo h\u1eb1ng \u0111\u1eb3ng th\u1ee9c th\u1ee9 hai: $(a-b)^2=a^2-2ab+b^2$.","explain":"<span class='basic_left'>Ta c\u00f3:<br\/> $(1-x)^2=1-2x+x^2$<span><br\/> <span class='basic_pink'> V\u1eady \u0111\u00e1p \u00e1n l\u00e0 B.<\/span>","column":2}]}],"id_ques":399},{"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/lv1/img\/1.png' \/><\/center>Khai tri\u1ec3n $(a+1)^2$ theo h\u1eb1ng \u0111\u1eb3ng th\u1ee9c ta \u0111\u01b0\u1ee3c:","select":["A. $a^2+2a+1$ ","B. $a^2-2a+1$ ","C. $a^2+a+1$","D. $a^2-a+1$"],"hint":"Khai tri\u1ec3n theo h\u1eb1ng \u0111\u1eb3ng th\u1ee9c th\u1ee9 nh\u1ea5t: $(a+b)^2=a^2+2ab+b^2$.","explain":"<span class='basic_left'> Ta c\u00f3:<br\/> $(a+1)^2=a^2+2a+1$<span><br\/> <span class='basic_pink'> V\u1eady \u0111\u00e1p \u00e1n l\u00e0 A.<\/span>","column":2}]}],"id_ques":400}],"lesson":{"save":0,"level":1}}