求下列因式分解

题目

求下列因式分解
(X+Y)平方-4(X-2Y)平方
(X-Y)平方*(X+Y)平方
12(M-N)平方+18)N-M)立方

答案

(X+Y)^2-4(X-2Y)^2
=[(X+Y)-2(X-2Y)][(X+Y)+2(X-2Y)]
=(-X+5Y)(3X-3Y)
=-3(X-5Y)(X-Y);
(X-Y)^2*(X+Y)^2
=[(X-Y)(X+Y)]^2
=(X^2-Y^2)^2
=X^4-2X^2Y^2+Y^4;

12(M-N)^2+18(N-M)^3
=12(N-M)^2+18(N-M)^3
=6(N-M)^2*[2+3(N-M)]
=6(N-M)^2*(3N-3M+2).