代数 (16 19:1:56) ⑴X²-Y²+X³-Y³ ⑵(a+1)(a+3)(a+5)(a+7)+15

问题描述:

代数 (16 19:1:56)
 ⑴X²-Y²+X³-Y³
 ⑵(a+1)(a+3)(a+5)(a+7)+15

因式分解
X²-Y²+X³-Y³
=(X-Y)(X+Y)+(X-Y)(X²+XY+Y²)
=(X-Y)(X²+XY+Y²+X+Y)
(a+1)(a+3)(a+5)(a+7)+15
设b=a-4
原式
=(b-1)(b+1)(b-3)(b+3)+15
=(b²-1)(b²-9)+15
=b^4-10b²+24
=(b²-4)(b²-6)
=(b-2)(b+2)(b-√6)(b+√ 6)
=(a+2)(a+6)(a-4-√6)(a-4+√6)
没有学过根号的话,就是(a+2)(a+6)(a²+8a+10)