81（x+y)^4-16(x-y)^4分解因式

题目

81（x+y)^4-16(x-y)^4分解因式

答案

原式=[9(x+y)²+4（x-y）²][9(x+y)²-4(x-y)²]
=(13x²+10xy+13y²){[3(x+y)+2(x-y)][3(x+y)-2(x-y)]}
=(13x²+10xy+13y²)(5x+y)(x+5y)