题目

1.（3x²+2x-8）²-（x²-2x-8）²
2.(x+2)(x+3)+x²-4
3.x²（a-b)+16(b-a)
4.（x²+2x）²-7（x²+2x)-8
5.(x²+9y²）²-36x²y²
6.（x-1）（x-2y-1)+y²

提问时间：2020-09-22

答案

1.
（3x²+2x-8）²-（x²-2x-8）²
=(3x²+2x-8+x²-2x-8)(3x²+2x-8-x²+2x+8)
=(4x²-16)(2x²+4x)
=8(x²-4)(x²+2x)
=8x(x+2)(x-2)(x+2)
=8x(x+2)^2(x-2)
2.
(x+2)(x+3)+x²-4
=x^2+5x+6+x^2-4
=2x^2+5x+2
=(x+2)(2x+1)
3.
x²（a-b)+16(b-a)
=(a-b)(x^2-16)
=(a-b)(x+4)(x-4)
4.
（x²+2x）²-7（x²+2x)-8
=(x^2+2x-8)(x^2+2x+1)
=(x-2)(x+4)(x+1)^2
5.
(x²+9y²）²-36x²y²
=(x²+9y²+6x²y²)(x²+9y²-6x²y²)
=(x+3y)^2(x-3y)^2
6.
（x-1）（x-2y-1)+y²
=x^2-2xy-x-x+2y+1+y²
=x^2-2xy+y²-2x+2y+1
=(x-y)^2-2(x-y)+1
=(x-y-1)^2