题目

因式分解 1、x+y+(x+y)^2-2 2、6x^2+xy-2y^2 3、(x-y)（x-y-3）+2 4、(x-1)x(x+1)(x+2)-24 希望有详细过程

提问时间：2020-07-29

答案

1.
x+y+(x+y)^2-2=(x+y+1/2)^2-9/4=(x+y-1)(x+y+2)
2.
十字相乘：2x -y
3x 2y
6x^2+xy-2y^2
=(2x-y)(3x+2y)
3.
把（x-y)当成一个整体,展开后再利用十字相乘法就可以具体是：原式=(x-y)[2(x-y)-3]-2
=2（x-y)(x-y)-3(x-y)-2
=(2x-2y+1)(x-y-2)
4.
x(x + 1)(x - 1)(x + 2) - 24
= x(x^2 - 1)(x + 2) - 24
= x(x^3 + 2x^2 - x - 2) - 24
= x^4 + 2x^3 - x^2 - 2x - 24
= (x^4 - 2x^3) + 4x^3 - x^2 - 2x - 24
= x^3(x - 2) + 4x^3 - 8x^2 + 7x^2 - 2x - 24
= (x^3 + 4x^2)(x - 2) + (7x^2 - 14x) + (12x - 24)
= (x^3 + 4x^2 + 7x + 12)(x - 2)
= [(x^3 + 3x^2) + (x^2 + 3x) + (4x + 12)](x - 2)
= (x^2 + x + 4)(x + 3)(x - 2)
希望可以帮到你o(∩_∩)o