f.2 maths (factorization)

1)
(2a+b)(x-y)-b(y-x)=(x-y)(2a+b+b)=2(x-y)(a+b)

2)
(5x+3y)(2x-y)-(y-x)(y-2x)=(2x-y)(5x+3y+y-x)=4(2x-y)(x+y)

3)
2ax-2bx-3ay+3by=2x(a-b)-3y(a-b)=(a-b)(2x-3y)

4)
8x^3-8x^2+4x-4=8x^2(x-1)+4(x-1)=4(x-1)(2x^2+1)

5)
a^2bc-a+ab^c-b-abc^2+c=abc(a+b-c)-(a+b-c)=(a+b-c)(abc-1)

6)
2ax-4ay-4bx+8by+6cx-12cy=2a(x-2y)-4b(x-2y)+6c(x-2y)=2(x-2y)(a-2b+3c)

7)
8x^3y^2 - 20x^2y^2 + 4xy^2
=4xy^2(2x^2-5x+1)
=4(3)(-1)
=-12

8)
6x^2y - 2x^3y - 2xy
=2xy(3x-x^2-1)
=-2xy(x^2-3x+1)
=-2(7)(2)
=-28

9)
1+m+n+mn=(1+m)+n(1+m)=(1+m)(1+n)

10)
1 + m + n + p + mn + mp +np +mnp
=(1+m+n+mn)+p(1+m+n+mn)
=(1+m+n+mn)(1+p)
=(1+m)(1+n)(1+p)

11)
(a+1)(a+2)=a^2+3a+2

12)
(x^2 + 3x)^2 + 3(x^2+3x) +2
=a^2+3a+2 (Let a=x^2+3x)
=(a+1)(a+2)
=(x^2+3x+1)(x^2+3x+2)
=(x^2+3x+1)(x+1)(x+2)