\(P=x^2-6xy+9y^2=\left(x-3y\right)^2\)

(Áp dụng 7 hằng đẳng thức đáng nhớ)

a) xy+xz-2y-2z=x(y+z)-2(y+z)=(y+z)(x-2)

b) \(x^2-6xy+9y^2-25z^2=\left(x-3y\right)^2-\left(5z\right)^2=\left(x-3y-5z\right)\left(x-3y+5z\right)\)

c) \(x^2-2x+2y-xy=x\left(x-2\right)+y\left(2-x\right)=x\left(x-2\right)-y\left(x-2\right)=\left(x-2\right)\left(x-y\right)\)

d) \(\left(x^2+1\right)^2-4x^2=\left(x^2+1-2x\right)\left(x^2+1+2x\right)=\left(x-1\right)^2\left(x+1\right)^2\)

e)\(x^2-y^2+2yz-z^2=x^2-\left(y^2-2yz+z^2\right)=x^2-\left(y-z\right)^2=\left(x+y-z\right)\left(x-y+z\right)\)

x²-xy-2y²

= x²-2xy+xy-2y²

=x(x-2y)+y(x-2y)

=(x-2y)(x+y)

\(x^2-6xy+9y^2=x^2-2.\left[x.\left(3y\right)\right]+\left(3y\right)^2\)

\(=\left(x-3y\right)^2\)

1)P= x² - 6xy+9y²

= (x-3y)^2

2) P= x⁴ - 64x

= (x^3 - 64) x

= (x^3 - 4^3)x

= (x^3 - 12x^2 + 48x - 64)x

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.

$3x^2-3y^2-12x+12y=(3x^2-3y^2)-(12x-12y)=3(x^2-y^2)-12(x-y)=3(x-y)(x+y)-12(x-y)=3(x-y)(x+y-4)$

\(\left(x+y+z\right)\left(xy+yz+xz\right)-xyz=xy\left(x+y+z\right)-xyz+\left(yz+xz\right)\left(x+y+z\right)\)

\(=xy\left(x+y+z-z\right)+z\left(x+y\right)\left(x+y+z\right)\)

\(=xy\left(x+y\right)+z\left(x+y\right)\left(x+y+z\right)\)

\(=\left(x+y\right)\left[xy+z\left(x+y+z\right)\right]\)

\(=\left(x+y\right)\left(xy+xz+yz+z^2\right)\)

\(=\left(x+y\right)\left[x\left(y+z\right)+z\left(y+z\right)\right]\)

\(=\left(x+y\right)\left(y+z\right)\left(x+z\right)\)