因式分解x^4-y^4+(x-y)(x+y)^3上面那个打错了x^4-y^4-(x-y)(x+y)^3

Question

因式分解 x^4-y^4+(x-y)(x+y)^3
上面那个打错了
x^4-y^4-(x-y)(x+y)^3

Answer 1

x^4-y^4-(x-y)(x+y)^3
=(x-y)(x+y)(x²+y²)-(x-y)(x+y)(x+y)²
=(x-y)(x+y)[(x²+y²)-(x+y)²]
=(x-y)(x+y)（-2xy)
=-2xy(x-y)(x+y)