分解因式 （1）x^2-4mx+8mn-4n^2 (2)x^4+64 (3)x^3-11x^2+31x-21 (5)x^3-4xy^2-2x^2y+8y^3
问题描述：
分解因式 （1）x^2-4mx+8mn-4n^2 (2)x^4+64 (3)x^3-11x^2+31x-21 (5)x^3-4xy^2-2x^2y+8y^3
答
（1）x^2-4mx+8mn-4n^2=(x+2n)(x-2n)-4m(x-2n)=(x-2n)(x+2n-4m)
(2)x^4+64=x^4+16x^2+64-16x^2=(x^2+8)^2-16x^2=(x^2+4x+8)(x^2-4x+8)
(3)x^3-11x^2+31x-21=x^3-x^2-10x^2+10x+21x-21=x^2(x-1)-10x(x-1)+21(x-1)
=(x-1)(x^6-10x+21)=(x-1)(x-3)(x-7)
(5)x^3-4xy^2-2x^2y+8y^3=(x+2y)(x^2-2xy+4y^2)-2xy(x+2y)=(x+2y)(x^2-4xy+4y^2)=(x+24)(x-2y)^2