3x2--3y2--12x+12y
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\(=3\left(x^2-y^2-x-y\right)\)
\(=3\left(x+y\right)\left(x-y-1\right)\)
b: \(x^2-6x+xy-6y\)
\(=x\left(x-6\right)+y\left(x-6\right)\)
\(=\left(x-6\right)\left(x+y\right)\)
c: \(2x^2+2xy-x-y\)
\(=2x\left(x+y\right)-\left(x+y\right)\)
\(=\left(x+y\right)\left(2x-1\right)\)
e: \(x^3-3x^2+3x-1=\left(x-1\right)^3\)
Lời giải:
1. $xy+xz-2y-2z=(xy+xz)-(2y+2z)$
$=x(y+z)-2(y+z)=(x-2)(y+z)$
2. $x^2-6xy+9y^2)-25z^2$
$=(x-3y)^2-(5z)^2=(x-3y-5z)(x-3y+5z)$
3.
$3x^2-3y^2-12x+12y=(3x^2-3y^2)-(12x-12y)=3(x^2-y^2)-12(x-y)=3(x-y)(x+y)-12(x-y)=3(x-y)(x+y-4)$
a: =3(x^2-y^2-4x+4y)
=3[(x-y)(x+y)-4(x-y)]
=3(x-y)(x+y-4)
b: \(=4x\left(x^2+y^2+2xy-16\right)\)
\(=4x\left[\left(x+y\right)^2-16\right]\)
\(=4x\left(x+y+4\right)\left(x+y-4\right)\)
c: \(=\left(x+4\right)^2-y^2=\left(x+4+y\right)\left(x+4-y\right)\)
d: \(=\left(x^2-1\right)\left(x^2-9\right)=\left(x-1\right)\left(x-3\right)\left(x+1\right)\left(x+3\right)\)
Ta có: 3x2 - 3y2 - 12x + 12y
= (3x2 - 3y2) - (12x - 12y)
= 3.(x2 - y2) - 12.(x - y)
= 3.(x - y).(x + y) - 4.3(x - y)
= 3.(x - y).(x + y - 4)