Question

把下列各式分解因式

(1) 3p平方（a-x)-2p²（x-a)
(2) 6m(p²-q）^三次方 + 4n ( q-p²）²
(3) a (x+y) +b (x+y) -c (x+y)
(4) 3a²b（2x-y）-6ab² （y-2x）

Answer 1

3p^2(a-x)-2p^2(x-a)
=3p^2(a-x)+2p^2(a-x)
=(a-x)(3p^2+2p^2)
=5p^2(a-x)

6m(p^2-q)^3+4n(q-p^2)^2
=6m(p^2-q)^3+4n(p^2-q)^2
=2(p^2-q)^2[3m(p^2-q)+2n]
=2(p^2-q)^2(3mp^2-3mq+2n)

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

3a^2b(2x-y)-6ab^2(y-2x)
=3a^2b(2x-y)+6ab^2(2x-y)
=3ab(2x-y)(a+2b)