Question

因式分解

1. (x-y)a-x+y 2. a²(a-b)+b²(b-a)
3. 2x³-16y³ 4. 3y²+9y-12
5. 5x²-13xy-6y² 6. x³-2x²-10x-20
7. -3x³-12x²+36x 8. 9-x²+12xy-36y²
9. 9s(s-1)-2t(6s-2t-3) 10. 6(m-n)²-10m+10n-4
11. -3y^4+10y²+8 12. 3x²y+28y²+7xy²+12xy
13. (a²-b²)+3(a²-b²)-18 14. a²+2ab+b²-a-b
15. (m²+3m)²-8(m²+3m)-20 16. 4a²bc-3a²c²+8abc-6ac²
17. (y²+3y)²-(2y+6)²

最好有步骤！我会追加分的！

Answer 1

1、(x-y)a-x+y
=(x-y)a-(x-y)
=(x-y)(a-1)
2、a²(a-b)+b²(b-a)
=a²(a-b)-b²(a-b)
=(a-b)(a²-b²)
=(a-b)(a-b)(a+b)
=(a-b)²(a+b)
3、2x³-16y³
=2(x³-8y³)
=2(x³-(2y)^3)
=2(x-2y)(x²+4y^4+2xy)
4、3y²+9y-12
=3(y²+3y-4)
=3(y+4)(y-1)
5、先解出方程5x²-13x-6=0的两根，为：x=3或-0.4于是有
5x²-13xy-6y²
=5(x-3)(x+0.4)
7、-3x³-12x²+36x
=-3x(x²+4x-12)
=-3x(x+6)(x-2)
自己做吧，第六题我怀疑是题目错了，第8、9、10题用待定系数法做

Answer 2

(x-y)a-x+y
=(x-y)a-(x-y)
=(x-y)(a-1)
a²(a-b)+b²(b-a)
=a²(a-b)-b²(a-b)
=(a-b)(a²-b²)
=(a-b)(a-b)(a+b)
=(a-b)²(a+b)