(x⁴+x²-4)(x⁴+x²+3)+10
问题描述:
(x⁴+x²-4)(x⁴+x²+3)+10
老师好像说是什么双十字相乘法,那一刻我没怎么学好.
答
(x⁴+x²-4)(x⁴+x²+3)+10
=(x⁴+x²)²-(x⁴+x²)-12+10
=(x⁴+x²)²-(x⁴+x²)-2
=(x⁴+x²+1)(x⁴+x²-2)
=(x⁴+2x²+1-x²)(x²-1)(x²+2)
=[(x²+1)²-x²](x²+2)(x²-1)
=(x²+1+x)(x²+1-x)(x²+2)(x+1)(x-1)
=(x²+x+1)(x²-x+1)(x²+2)(x+1)(x-1)