分解因式1.(2m-n)^2-(m-2n)^2 2.49(2a-3b)^2-9(a+b)^2 3.xy(x+y)-4x^3y^3

Question

分解因式1.(2m-n)^2-(m-2n)^2 2.49(2a-3b)^2-9(a+b)^2 3.xy(x+y)-4x^3y^3

Answer 1

原式=(2m-n)^2-(m-2n)^2
=[(2m-n)-(m-2n)][(2m-n)+(m-2n)]
=3(m+n)(m-n)
2.原式=49(2a-3b)^2-9(a+b)^2
=[7(2a-3b)]^2-[3(a+b)]^2
=[7(2a-3b)-3(a+b)][7(2a-3b)+3(a+b)]
=(11a-24b)(17a-18b)
3.原式=xy(x+y)-4x^3y^3
=xy(x+y-4x²y²)