Question

(a-2b)(a+2b)(a^2+2ab+4b^2)(a^2-2ab+4b^2)

化简 注意是2ab

Answer 1

答：
(a-2b)(a+2b)(a²+2ab+4b²)(a²-2ab+4b²)
=(a²-4b²) [ (a²+4b²)²-(2ab)² ]
=(a²-4b²) ( a^4+8a²b²+16b^4-4a²b²)
=(a²-4b²) (a^4+4a²b²+16b^4)
=(a²)³-(4b²)³
=a^6-64b^6

最后三步利用到立方差公式

Answer 2

(a-2b)(a+2b)(a²+2ab+4b²)(a²-2ab+4b²)
=(a-2b)(a+2b)(a+2b)²(a-2b)²
=(a-2b)³(a+2b)³

用完全平方公式,4b²就是(2b)²