题目

计算题：(a+b+c)的平方-(a+b)的平方-(b+c)的平方
还有几道
x的四次方+2x³+2x²+2x+1
x的9次方+x的6次方+x的3次方-3
3x³-8x²-9

提问时间：2020-07-24

答案

(a+b+c)²-(a+b)²-(b+c)²
=(a+b)²+c²+2(a+b)c-(a+b)²-(b²+c²+2bc）
=c²+2ac+2bc-b²-c²-2bc
=2ac-b²
x^9+x^6+x^3 -3
=(x^9-x^6)+(2x^6+x^3 -3)
=x^6(x^3-1)+(x^3-1)(2x^3+3)
=(x^3-1)(x^6+2x^3+3)
=(x-1)(x²+x+1)(x^6+2x^3+3)
x^4+2x³+2x²+2x+1
=x^4+2x³+x²+x²+2x+1
=x²(x²+2x+1)+(x²+2x+1)
=(x²+1)(x²+2x+1)
=(x²+1)(x+1)²
3x³-8x²-9
=3x³-9x²+x²-9
=3x²(x-3)+(x+3)(x-3)
=(3x²+x+3)(x-3)