题目

1.64x^3+1
2.81-27y^3
3.3x^3-24
4.(p^n+3)-p^n
5.(a^n+6)+a^n
6.(x-y)^3+8y^3
7.(a+b)^3-b^3
8.(x^3-1)(x^3+1)-8
9.1-8(x+y)^3
10.a^6-b^6
11.3x^9 - 192 x^3 y^6
12.1+1/8a^3b^3
^是根号.

提问时间：2021-03-13

答案

1.64x^3+1
=（4x+1)(16x^2-4x+1)
2.81-27y^3
=27（3－y^3）
3.3x^3-24
=3（x-2)(x^2+2x+4)
4.(p^n+3)-p^n
=p^n(p-1)(p^2+p+1)
5.(a^n+6)+a^n
=a^n(a^2+1)(a^2+a+1)(a^2-a+1)
6.(x-y)^3+8y^3
=(x+y)(x^2-4xy+7y^2)
7.(a+b)^3-b^3
=a(a^2+3ab+3b^2)
8.(x^3-1)(x^3+1)-8
=(x^3+3)(x^3-3）
9.1-8(x+y)^3
=(1-2x-2y)(4x^2+8xy+4y^2+2x+2y+1)
10.a^6-b^6
=(a+b)(a-b)(a^2+ab+b^2)(a^2-ab+b^2)
11.3x^9 - 192 x^3 y^6
=3x^3(x-2y)(x+2y)(x^2-2xy+4y^2)(x^2+2xy+4y^2)
12.1+1/8a^3b^3
=(1/2ab+1)(1/4a^2b^2-1/2ab+1)
我写了这么多才发现,这不就是经典的立方和,立方差公式的变形题吗?
a^3+b^3=（a+b)(a^2-ab+b^2)
a^3-b^3=（a-b)(a^2+ab+b^2)