8a的四次方—2a²b²,-（x²-y²)(x+y)-(y-x)³,a的四次方-81b的四次方,因式分解
问题描述：
8a的四次方—2a²b²,-（x²-y²)(x+y)-(y-x)³,a的四次方-81b的四次方,因式分解
答
8a^4-2a²b²
=2a²(4a²-b²)
=2a²(2a+b)(2a-b)
-(x²-y²)(x+y)-(y-x)³
=-[(x+y)(x-y)](x+y)+(x-y)³
=-(x-y)(x+y)²+(x-y)³
=(x-y)[(x-y)²-(x+y)²]
=(x-y)[(x-y)+(x+y)][(x-y)-(x+y)]
=-4xy(x-y)
a^4-81b^4
=(a²+9b²)(a²-9b²)
=(a²+9b²)(a+3b)(a-3b)