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1 ) \(x^3-x^2y-xy+y^2\)
\(=\left(x^3-x^2y\right)-\left(xy-y^2\right)\)
\(=x^2.\left(x-y\right)-y.\left(x-y\right)\)
\(=\left(x-y\right).\left(x^2-y\right)\)
2 ) \(x^2-2xy+x-2y\)
\(=\left(x^2+x\right)-\left(2xy+2y\right)\)
\(=x.\left(x+1\right)-2y.\left(x+1\right)\)
\(=\left(x+1\right).\left(x-2y\right)\)
3 ) \(x^2+4xy+3y^2\)
\(=x^2+3xy+xy+3y^2\)
\(=\left(x^2+3xy\right)+\left(xy+3y^2\right)\)
\(=x.\left(x+3y\right)+y.\left(x+3y\right)\)
\(=\left(x+3y\right).\left(x+y\right)\)
=(3x+3y)-(x^2+2xy+y^2)=3(x+y)-(x+y)^2=k rõ nữa
=(4x^2-4xy) -(6y^2-6xy)= 4x(x-y)+6y(x-y)=2(x-y)(2x+3y)
a) xy – 3x + 2y – 6
= (xy - 3x) + (2y - 6)
= x(y - 3) + 2(y - 3)
= (y - 3)(x + 2)
b) x2y + 4xy + 4y – y3
= y(x2 + 4x + 4 - y2)
= y[(x2 + 4x + 4) - y2]
= y[(x + 2)2 - y2]
= y(x + 2 + y)(x + 2 - y)
c) x2 + y2 + xz + yz + 2xy
= (x2 + 2xy + y2) + (xz + yz)
= (x + y)2 + z(x + y)
= (x + y)(x + y + z)
d) x3 + 3x2 – 3x – 1
= (x3 - 1) + (3x2 - 3x)
= (x - 1)(x2 + x + z) + 3x(x - 1)
= (x - 1)(x2 + 4x + 1)
a )
\(xy-3x+2y-6\)
\(=\left(xy+2y\right)-3x-6\)
\(=y\left(x+2\right)-3\left(x+2\right)\)
\(=\left(y-3\right)\left(x+2\right)\)
b )
\(x^2y+4xy+4y-y^3\)
\(=y\left(x^2+4x+4-y^2\right)\)
\(=y\left[\left(x+2\right)^2-y^2\right]\)
\(=y\left(x+2-y\right)\left(x+2+y\right)\)
c )
\(x^2+y^2+xz+yz+2xy\)
\(=\left(x+y\right)^2+z\left(x+y\right)\)
\(=\left(x+y\right)\left(x+y+z\right)\)
a/ \(=3y^2-6y-2x+1\)
b/ \(=-\left(x^3-3x^2+3x-1\right)=-\left(x-1\right)^3\)
c/ \(=\left(2-x\right)^3\)
d/ \(=xy^2+x^2y+3xy+x^2y+x^3+3x^2-3xy-3x^2-9x\)
\(=xy\left(y+x+3\right)+x^2\left(y+x+3\right)-3x\left(y+x+3\right)\)
\(=\left(xy+x^2-3x\right)\left(y+x+3\right)=x\left(y+x-3\right)\left(y+x+3\right)\)
e/ \(=xy-x^2+2x-y^2+xy-2y\)
\(=x\left(y-x+2\right)-y\left(y-x+2\right)=\left(x-y\right)\left(y-x+2\right)\)
a) =(2x+3y-1)2
b)=-(x-1)3
c)=-(x3-6x2+12x-8)=-(x-2)3
d)x3 + 2x2y + xy2 – 9x
= x(x2 + 2xy + y2 -9)
= x[(x2 + 2xy + y2) - 32]
= x[(x + y)2 - 32]
= x (x + y – 3)(x + y + 3)
e) 2x-2y-x2+2xy-y2=2(x-y)-(x-y)2=(x-y)(2-x+y)
a) x^4 - x^3 - x + 1
= x^3 ( x - 1 ) - ( x- 1 )
= ( x^3 - 1 )(x - 1)
= ( x- 1 )^2 (x^2 + x + 1 )
a)x4-x3-x+1
=x3(x-1)-(x-1)
=(x-1)(x3-1)
=(x-1)(x-1)(x2+x+1)
=(x-1)2(x2+x+1)
b)5x2-4x+20xy-8y
(sai đề)
c) 2x^3y - 2xy^3 - 4xy^2 - 2xy
= 2xy ( x^2 - y^2 - 2y - 1 )
= 2xy ( x^2 - ( y^2 + 2y + 1 )
= 2xy ( x^2 - ( y + 1 )^2 )
= 2x ( x - y - 1 )( x + y + 1 )
sai bạn ơi !
đáp án là
= 2xy (x + y + 1) (x - y + 1)
that pun cho ban Nguyen Dieu Thao :((
1)\(=x^2\left(x-y\right)-y\left(x-y\right)\\ =\left(x-y\right)\left(x^2-y\right)\)
2)\(=\left(x^2+x\right)-\left(2xy+2y\right)\\ =x\left(x+1\right)-2y\left(x+1\right)\\ =\left(x+1\right)\left(x-2y\right)\)
3)\(=\left(x^2+2.x.2y+4y^2\right)-y^2\\ =\left(x+2y\right)^2-y^2\\ =\left(x+2y+y\right)\left(x+2y-y\right)\)
1) x3 - x2y - xy + y2
= (x3 - x2y) - (xy - y2)
= x2.(x - y) - y.(x - y)
= (x - y).(x2 - y)
2) x2 - 2xy + x - 2y
= (x2 + x) - (2xy + 2y)
= x.(x + 1) - 2y.(x + 1)
= (x + 1).(x - 2y)
3) x2 + 4xy + 3y2
= x2 + 3xy + xy + 3y2
= (x2 + 3xy) + (xy + 3y2)
= x.(x + 3y) + y.(x + 3y)
= (x + 3y).(x + y)