Question

因式分解，急求。1，a^5(2a-1)^2-2a^3(2a-1)^3+a(2a-1)^4 2，2(a^2+b^2)(a+b)^2-(a^2-b^2)^2

3，x^2(a^2-b^2)-6x(a^2-b^2)-9(b^2-a^2)

Answer 1

1，a^5(2a-1)^2-2a^3(2a-1)^3+a(2a-1)^4
=a(2a-1)²[a^4-2a²(2a-1)+(2a-1)²]
=a(2a-1)²(a²-2a+1)²
=a(2a-1)²(a-1)^4

2，2(a^2+b^2)(a+b)^2-(a^2-b^2)^2
=2(a²+b²)(a+b)²-(a+b)²(a-b)²]
=(a+b)²(2a²+2b²-a²+2ab-b²)
=(a+b)²(a²+2ab+b²)
=(a+b)^4

3，x^2(a^2-b^2)-6x(a^2-b^2)-9(b^2-a^2)
=x²(a²-b²)-6x(a²-b²)+9(a²-b²)
=(a²-b²)(x²-6x+9)
=(a+b)(a-b)(x-3)²