题目

高一衔接知识,因式分解 2.8x^3+4x^2-2x-1 3.5x^2-15x+2xy-6y 4.4xy+1-4x^2-y^2
5.a^4b-a^3b^2-a^2b^2-ab^4
6.x^2(x+1)-y(xy+x)
7.x^6-y^6-2x^3+1

提问时间：2020-11-15

答案

2、8x^3+4x^2-2x-1
=4x²(2x+1)-(2x+1)
=(2x+1)(4x²-1)
=(2x+1)²(2x-1)
3.5x^2-15x+2xy-6y
=5x(x-3)+2y(x-3)
=(x-3)(5x+2y)
4.4xy+1-4x^2-y^2
=1-(4x²-4xy+y²）
=1-（2x-y)²
=（1+2x-y)(1-2x+y)
5.a^4b-a^3b^2-a^2b^2-ab^4
=ab(a³-a²b-ab-b³）
6.x^2(x+1)-y(xy+x)
=x³+x²-xy²-xy
=x³-xy²+x²-xy
=x(x+y)(x-y)+x(x-y)
=x(x-y)(x+y+1)
7.x^6-y^6-2x^3+1
=(x³-1)²-y^6
=(x³-1+y³)(x³-1-y³)