Question

把下列各式分分解因式

1.x（a-b）+y（b-a） 2.ab+b²-ac-bc 3.x²-2x-8 4.3x²+5x-2 5.（a+b）²x²-2（a²+b²）xy+（a-b）²y² 6.-a²-b²+2ab+4 7.3x²+11x+10 8.5x²-6xy-8y²

Answer 1

1.x（a-b）+y（b-a）
=x(x-b)-y(a-b)
=(a-b)(x-y)

2.ab+b²-ac-bc
=b(a+b)-c(a+b)
=(a+b)(b-c)

3.x²-2x-8
=(x-4)(x+2)

4.3x²+5x-2
=(3x-1)(x+2)

5.（a+b）²x²-2（a²-b²）xy+（a-b）²y² 中间换了一个减号
=[(a+b)x-(a-b)y]²
=(ax+bx-ay+by)²

6.-a²-b²+2ab+4
=4-(a²-2ab+b²)
=4-(a-b)²
=(2+a-b)(2-a+b)

7.3x²+11x+10
=(3x+5)(x+2)

8.5x²-6xy-8y²
=(5x+4y)(x-2y)

Answer 2

1.=(x-y)(a-b)
2.=b(a+b)-c(a+b)=(b-c)(a+b)
3.=(x-4)(x+2)
4.=(x-2)(3x+1)
5.=(a²+b²)(x²+y²)+2abx²-2(a²+b²)xy-2aby²
=(a²+b²)(x-y)²+2ab(x+y)(x-y)
=(x-y)((a²+b²)(x-y)+2ab(x+y))
6.=4-(a-b)^2=(2+a-b)(2-a+b)
7.=(x+2)(3x+5)
8.=(x-2y)(5x+4y)