Question

2道因式分解、急~

1. （x+1)²-9(x-1)²
2. 4a²b²-（a²+b²-c²)²

Answer 1

1. （x+1)²-9(x-1)²
＝[（x+1)+3(x-1)][(x+1)-3(x-1)]
=(4x-2)(-2x+4)
=-4(x-2)(x-2)
=-4(x-2)²

2. 4a²b²-（a²+b²-c²)²
=[2ab+(a²+b²-c²)][2ab-(a²+b²-c²)]
=[(a+b)²-c²][c²-(a-b)²]
=(a+b+c)(a+b-c)(c+a-b)(c-a+b)

Answer 2

(x+1)²-9(x-1)²=(x+1+3x-3)(x+1-3x+3)=4(2x-1)(-x+2)
4a²b²-（a²+b²-c²)²=(2ab+a²+b²-c²)(2ab-a²-b²+c²)
=((a+b)²-c²)(-(a-b)²+c²)
=(a+b+c)(a+b-c)(a-b+c)(-a+b+c)