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\(1,=x\left(x^2-2x+1-y^2\right)=x\left[\left(x-1\right)^2-y^2\right]=x\left(x-y-1\right)\left(x+y-1\right)\\ 2,=\left(x+y\right)^3\\ 3,=\left(2y-z\right)\left(4x+7y\right)\\ 4,=\left(x+2\right)^2\\ 5,Sửa:x\left(x-2\right)-x+2=0\\ \Leftrightarrow\left(x-2\right)\left(x-1\right)=0\Leftrightarrow\left[{}\begin{matrix}x=1\\x=2\end{matrix}\right.\)
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a) x2 - xy - 20y2
= x2 + 4xy - 5xy - 20y2
= x( x + 4y ) - 5y( x + 4y )
= ( x + 4y )( x - 5y )
b) x3 - x2y - 3xy2 + 2y3
= x3 + x2y - 2x2y - xy2 - 2xy2 + 2y3
= ( x3 + x2y - xy2 ) - ( 2x2y + 2xy2 - 2y3 )
= x( x2 + xy - y2 ) - 2y( x2 + xy - y2 )
= ( x2 + xy - y2 )( x - 2y )
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That so easy bài này chệ làm rồi :))))))) mới lớp 7
x4+2x3+3x2+2x+1x4+2x3+3x2+2x+1
Đặt y=x2+1y=x2+1, ta có :
A=x4+2x3+3x2+2x+1A=x4+2x3+3x2+2x+1
=x4+2x2+1+x2+2x+2x3=x4+2x2+1+x2+2x+2x3
=(x2+1)2+2x(x2+1)+x2=(x2+1)2+2x(x2+1)+x2
=y2+2xy+x2=y2+2xy+x2
=(x+y)2=(x2+x+1)
Mấy bài này that so easy
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x3 - x + 3x2y + 3xy2 + y3 - y ( sửa -x3 -> x3 )
= ( x3 + 3x2y + 3xy2 + y3 ) - ( x + y )
= ( x + y )3 - ( x + y )
= ( x + y )[ ( x + y )2 - 1 ]
= ( x + y )( x + y - 1 )( x + y + 1 )
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a) 3xy2 + x2y2 - 5x2y = xy( 3y + xy - 5x )
b) 8m3 + 12m2 + 6m + 1 = ( 2m + 1 )3
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a) \(=2\left(x-y\right)-\left(x^2-2xy+y^2\right)\)
\(=2\left(x-y\right)-\left(x-y\right)^2\)
\(=\left(x-y\right)\left(2-x+y\right)\)
b) \(x^3-x+3x^2y+3xy^2+y^3-y\)
\(=\left(x^3+y^3\right)+\left(3x^2+3xy^2\right)-\left(x+y\right)\)
\(=\left(x+y\right)\left(x^2-xy+y^2\right)+3xy\left(x+y\right)-\left(x+y\right)\)
\(=\left(x+y\right)\left(x^2-xy+y^2+3xy-1\right)\)
\(=\left(x+y\right)\left(x^2+y^2+2xy-1\right)\)
a, x2 + 2y2 - 3xy + x - 2y = x2 - 4xy + 4y2 + xy - 2y2 + x - 2y
= ( x - 2y )2 + y( x - 2y ) + ( x - 2y )
= ( x - 2y )( x - 2y + y + 1 )
( x - 2y )( x - y + 1 )