把下列各式进行因式分解:

题目

把下列各式进行因式分解:
(1)-4x^2y^2-2xy
(2)4a^2 - 1/100 b^2
(3)m(a-b)-n(a-b)
(4)m(x-y)^2+n(y-x)^3
(5)32a^5-2a
(6)9(x+y)^2-4(x-y)^2

答案

(1)-4x^2y^2-2xy
=-2xy(2xy+1)[提公因式]
(2)4a^2 - 1/100 b^2
=（2a+1/10b）(2a-1/10b)[平方差公式]
(3)m(a-b)-n(a-b)
=(m-n)(a-b)[提公因式]
(4)m(x-y)^2+n(y-x)^3
(y-x)^2(m+ny-nx)[提公因式]
(5)32a^5-2a
=2a(16a^4-1)
=2a(4a^2+1)(4a^2-1)
=2a(4a^2+1)(2a+1)(2a-1)[提公因式,平方差公式]
(6)9(x+y)^2-4(x-y)^2
=（3x+3y-2x+2y）(3x+3y+2x-2y)
=(x+5y)(y+5x)[平方差公式]