Question

因式分解1:(x^2-9y^2)-(x+3y)

因式分解2：(a-b)^4-(b-a)^2
速度啊

Answer 1

1:(x^2-9y^2)-(x+3y)
=（x+3y）（x-3y）-(x+3y)
=(x+3y)(x-3y-1)
提取公因式

2：(a-b)^4-(b-a)^2
=(a-b)^4-(a-b)^2
=(a-b)^2[(a-b)^2-1]
=(a-b)^2(a-b+1)(a-b-1)
提取公因式后再应用平方差公式

Answer 2

(x^2-9y^2)-(x+3y)
=(x+3y)(x-3y)-(x+3y)
=(x+3y)(x-3y-1)

(a-b)^4-(b-a)^2
=(a-b)²[(a-b)²-1]
=(a-b)²(a-b+1)(a-b-1)