a: (x^2+x)^2+4x^2+4x-12

=(x^2+x)^2+4(x^2+x)-12

=(x^2+x+6)(x^2+x-2)

=(x^2+x+6)(x+2)(x-1)

b: =(x^2+8x)^2+22(x^2+8x)+105+15

=(x^2+8x)^2+22(x^2+8x)+120

=(x^2+8x+10)(x^2+8x+12)

=(x^2+8x+10)(x+2)(x+6)

c: =8x^2+12x-2x-3

=(2x+3)(4x-1)

a/ \(\left(x+y\right)^2-8\left(x+y\right)+12\)

\(=\left(x+y\right)\left(x+y-8+12\right)\)

\(=\left(x+y\right)\left(x+y+4\right)\)

==========

b/\(\left(x^2+2x\right)^2-2x^2-4x-3\)

\(=\left(x^2+2x\right)^2-\left(2x^2+4x\right)-3\)

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

\(=\left(x^2+2x\right)\left(x^2+2x-5\right)\)

===========

c/ \(\left(x^2+x\right)^2-2\left(x^2+x\right)-15\)

\(=\left(x^2+x\right)\left(x^2+x-2-15\right)\)

\(=\left(x^2+x\right)\left(x^2+x-17\right)\)

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a: \(x^4-4x^3-8x^2+8x\)

\(=x\left(x^3-4x^2-8x+8\right)\)

\(=x\left[\left(x+2\right)\left(x^2-2x+4\right)-4x\left(x+2\right)\right]\)

\(=x\left(x+2\right)\left(x^2-6x+4\right)\)

b: \(x^2-1-xy+y\)

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

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

c: Ta có: \(\left(x-1\right)\left(x-2\right)\left(x-3\right)+\left(x-1\right)^2\cdot\left(x-2\right)\)

\(=\left(x-1\right)\cdot\left(x-2\right)\cdot\left(x-3-x-1\right)\)

\(=2\cdot\left(x-1\right)\cdot\left(x-2\right)^2\)

a: \(x^2-y^2-x-y\)

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

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

f: \(x^3-5x^2-5x+1\)

\(=\left(x+1\right)\left(x^2-x+1\right)-5x\left(x+1\right)\)

\(=\left(x+1\right)\left(x^2-6x+1\right)\)

a) = 2(x-2)^2

b) = 4(x - y) + (x - y)(x + y)

= (x - y)(x + y + 4)

c) = (x - 2)(x - 4)

\(2\left(x-2\right)^2\)

\(\left(4+x+y\right)\left(x-y\right)\)

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

b) \(\left(x^2+x\right)^2+4x^2+4x-12=\left(x^2+x\right)^2+4\left(x^2+x\right)+4-16=\left(x^2+x+2\right)^2-4^2=\left(x^2+x+2-4\right)\left(x^2+x+2+4\right)=\left(x^2+x-2\right)\left(x^2+x+6\right)=\left(x-1\right)\left(x+2\right)\left(x^2+x+6\right)\)

c) \(\left(x+2\right)\left(x+3\right)\left(x+4\right)\left(x+5\right)-24=\left(x^2+7x+10\right)\left(x^2+7x+12\right)-24=\left(x^2+7x+10\right)^2+2\left(x^2+7x+10\right)+1-25=\left(x^2+7x+11\right)^2-5^2=\left(x^2+7x+11-5\right)\left(x^2+7x+11+5\right)=\left(x^2+7x+6\right)\left(x^2+7x+16\right)=\left(x+1\right)\left(x+6\right)\left(x^2+7x+16\right)\)

a. \(x^2\left(x^2+4\right)-x^2-4\)

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

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

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

b. \(\left(x^2+x\right)^2+4x^2+4x-12\)

\(=x^4+2x^3+5x^2+4x-12\)

\(=\left(x-1\right)\left(x+2\right)\left(x^2+x+6\right)\)

c. \(\left(x+2\right)\left(x+3\right)\left(x+4\right)\left(x+5\right)-24\)

\(=\left(x+2\right)\left(x+5\right)\left(x+3\right)\left(x+4\right)-24\)

\(=\left(x^2+7x+10\right)\left(x^2+7x+12\right)-24\) (*)

Đặt \(t=x^2+7x+10\), ta được

(*) \(=t\left(t+2\right)-24\)

\(=t^2+2t-24\)

\(=\left(t-4\right)\left(t+6\right)\)

hay \(\left(x^2+7x+6\right)\left(x^2+7x+18\right)\)

a, 7x - 14

= 7(x-2)

b, 2x - 2y + \(x^2\)- xy 

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

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

= (x-y)(2+x)

c, 6x + 12

= 6(x+2)

\(a,=7\left(x-2\right)\\ b,=2\left(x-y\right)+x\left(x-y\right)=\left(x+2\right)\left(x-y\right)\\ c,=6\left(x+2\right)\\ d,\text{Sai đề}\)