Question

因式分解 几道题目 求解！

(1)(x+y)^2-4(x+y)-12

(2)12(x+y)^2+11(x+y)(x-y)+2(x-y)^2

(3)5+7(a+1)-6(a+1)^2

(4)(a-2b)^2-8(a-2b)+12

(5)x^6-19x^3y^3-216y^6

(6)(x^2+x+4)^2+8x(x^2+x+4)+15x^2

(7)(x^2+x)^2-14(x^2+x)+24

题目比较多，如能解答 必将重谢

Answer 1

(1)(x+y)^2-4(x+y)-12=(x+y-6)(x+y+2)
(2)12(x+y)^2+11(x+y)(x-y)+2(x-y)^2=[3(x+y)+2(x-y)]*[4(x+y)+x-y]=(5x+y)(5x+3y)
(3)5+7(a+1)-6(a+1)^2=[5-3(a+1)]*[1+2(a+1)]=(2-3a)(3+2a)
(4)(a-2b)^2-8(a-2b)+12=(a-2b-2)(a-2b-6)
(5)x^6-19x^3y^3-216y^6=(x^3-27y^3)(x^3+8y^3)
(6)(x^2+x+4)^2+8x(x^2+x+4)+15x^2=(x^2+x+4+3x)(x^2+x+4+5x)=(x^2+4x+4)(x^2+6x+4)
(7)(x^2+x)^2-14(x^2+x)+24=(x^2+x-2)(x^2+x-12)=(x+2)(x-1)(x+4)(x-3)