a,x²-y²-2x+2y
= (x+y)(x-y) - 2(x-y)
= (x-y)(x+y-2)
b,2x+2y-x²-xy
= 2(x+y) - x(x+y)
= (x+y)(2-x)
c,3a²-6ab+3b²-12c²
= 3(a² - 2ab + b² - 4c²)
= 3[(a-b)² - 4c²)
= 3(a-b-2c)(a-b+2c)
d,x²-25+y²+2xy
= (x+y)² - 25
= (x+y+5)(x+y-5)

e) a²+2ab+b²-ac-bc

= (a+b)²-c(a+b)

= (a+b)( a+b-c)

f) x²-2x-4x²-4y

= -3x²-2x-4y

= -(3x²+2x+4y)

g)x²y-x³-9y+9x

= x²(y-x)-9(y-x)

= (y-x)(x²-9)

h) x²(x-1)+16(1-x)

= x²(x-1)-16(x-1)

= (x-1)(x²-16)

= (x-1)(x-4)(x+4)

n) 81x²-6yz-9y²-z²

= (9x)²-[(3y)²+6yz+z²]

=(9x)²-(3y+z)²

=(9x+3y+z)(9x-3y-z)

m) xz- yz-x²+2xy-y²

= z(x-y)-(x²-2xy+y²)

= z(x-y)-(x-y)²

= (x-y)(z-x+y)

 p) x² + 8x + 15

= x² + 3x + 5x + 15

= x(x+3) + 5(x+3)

= (x+3)(x+5)

k) x² - x - 12

= x² + 3x - 4x - 12

= x(x+3) - 4(x+3)

= (x+3)(x-4)

a: \(3abc^3-6a^2b^3c+12a^3bc\)

\(=3abc\cdot c^2-3abc\cdot2ab^2+3abc\cdot4a^2\)

\(=3abc\left(c^2-2ab^2+4a^2\right)\)

b: \(27-8y^3\)

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

\(=\left(3-2y\right)\left(9+6y+4y^2\right)\)

c: Sửa đề: \(4x^2+4x-y^2+1\)

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

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

\(=\left(2x+1+y\right)\left(2x+1-y\right)\)

d: \(3a^2\cdot\left(x-2\right)-6ab\cdot\left(2-x\right)\)

\(=3a^2\cdot\left(x-2\right)+6ab\cdot\left(x-2\right)\)

\(=\left(x-2\right)\left(3a^2+6ab\right)\)

\(=3a\left(a+2b\right)\left(x-2\right)\)

\(5a^2-14ab-3b^2\\ =5a^2-15ab-ab-3b^2\\ =5a\left(a-3b\right)-b\left(a-3b\right)\\ =\left(5a-b\right)\left(a-3b\right)\)

\(5a^2-14ab-3b^2\)

\(=5a^2-15ab+ab-3b^2\)

\(=5a\left(a-3b\right)+b\left(a-3b\right)\)

\(=\left(a-3b\right)\left(5a+b\right)\)

​\(9a^2b+6ab^2+b^3-6ab-2b^2\)

\(=b\left(9a^2+6ab+b^2-6a-2b\right)\)

\(=b\left[\left(3a+b\right)^2-2\left(3a+b\right)\right]\)

\(=b\left(3a+b\right)\left(3a+b-2\right)\)

\(=b\left(9a^2+6ab+b^2\right)-2b\left(3a+b\right)\)

\(=b\left(3a+b\right)^2-2b\left(3a+b\right)\)

\(=b\left(3a+b\right)\left(3a+b-2\right)\)

\(9a^2b+6ab^2+b^3-6ab-2b^2\)

\(=b\left(9a^2+6ab+b^2-6a-2b\right)\)

\(=b\left[\left(3a+b\right)^2-2\left(3a+b\right)\right]\)

\(=b\left(3a+b\right)\left(3a+b-2\right)\)

a^3+b^3+6ab-8=

\(\left(a+b-2\right)\left(b^2-ab+2b+a^2+2a+4\right)\)

có thể kỹ hơn không ạ?

b: \(2x^2-7xy+3y^2+x-3y\)

\(=2x^2-6xy-xy+3y^2+x-3y\)

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

\(=\left(x-3y\right)\left(2x-y+1\right)\)

Lời giải:
a.

Đặt $2a^2+5ab-3b^2-7b-2=(a+mb+n)(2a+pb+k)$ với $m,n,p,k$ nguyên 

$\Leftrightarrow 2a^2+5ab-3b^2-7b-2=2a^2+ab(2m+p)+mpb^2+a(k+2n)+b(km+np)+kn$ 

Đồng nhất hệ số:

\(\left\{\begin{matrix} 2m+p=5\\ mp=-3\\ k+2n=0\\ km+np=-7\\ kn=-2\end{matrix}\right.\)

Giải hpt này ta thu được $m=3; n=1; p=-1; k=-2$

Vậy $2a^2+5ab-3b^2-7b-2=(a+3b+1)(2a-b-2)$

b. Đa thức không phân tích được thành nhân tử

lm theo pp đồng nhất hệ số ạ

b: Ta có: \(2x^2-7xy+3y^2+x-3y\)

\(=2x^2-6xy-xy+3y^2+x-3y\)

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

\(=\left(x-3y\right)\left(2x-y+1\right)\)

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a^3+b^3+6ab-8=(a + b - 2) (a² - a b + 2a + b² + 2b + 4)