Question

【因式分解】.

① y²（x²-2x）³+y²
②a^（n+2）+a^（n+1）b-6a^nb²
③7（a+b）²-5（a+b）-2

过程。！

Answer 1

① y²（x²-2x）³+y²
=y²[(x²-2x)³+1]
=y²(x-1)²(x^4-4x³+3x²+2x+1_
②a^（n+2）+a^（n+1）b-6a^nb²
=a^n(a²+ab-6b²)
=a^n(a+3b)(a-2b)
③7（a+b）²-5（a+b）-2
=(7a+7b+2)(a+b-1)

Answer 2

① y²（x²-2x）³+y²
=y²(x²-2x+1)
=y²(x-1)²
②a^（n+2）+a^（n+1）b-6a^nb²
=a^(n+2)+b(a^(n+1))-6b²(a^n)
=(a²)(a^n)+(ab)(a^n)-(6b²)(a^n)
=(a²+ab-6b²)(a^n)
=(a+3b)(a-2b)(a^n)
③7（a+b）²-5（a+b）-2
=(7(a+b)+2)((a+b)-1)