神马作文网两道多项式计算(a+2b)(a-2b)[(a+2b)^2-6ab][(a-2b)^2+6ab](a-1)(a^4+a^3
来源：学生作业帮 编辑：神马作文网作业帮 分类：数学作业 时间：2024/11/10 03:10:31
两道多项式计算
(a+2b)(a-2b)[(a+2b)^2-6ab][(a-2b)^2+6ab]
(a-1)(a^4+a^3+a^2+a+1)
前面那题我钻研出来了，方法和你一样，后面的我就卡在(a-1)[a^3(a+1)+a(a+1)+1)]
这一步上了，我去验证一下……再回来给你加最佳……
(a+2b)(a-2b)[(a+2b)^2-6ab][(a-2b)^2+6ab]
(a-1)(a^4+a^3+a^2+a+1)
前面那题我钻研出来了，方法和你一样，后面的我就卡在(a-1)[a^3(a+1)+a(a+1)+1)]
这一步上了，我去验证一下……再回来给你加最佳……
![两道多项式计算(a+2b)(a-2b)[(a+2b)^2-6ab][(a-2b)^2+6ab](a-1)(a^4+a^3](/uploads/image/z/18534877-61-7.jpg?t=%E4%B8%A4%E9%81%93%E5%A4%9A%E9%A1%B9%E5%BC%8F%E8%AE%A1%E7%AE%97%28a%2B2b%29%28a-2b%29%5B%28a%2B2b%29%5E2-6ab%5D%5B%28a-2b%29%5E2%2B6ab%5D%28a-1%29%28a%5E4%2Ba%5E3)
(a+2b)(a-2b)[(a+2b)^2-6ab][(a-2b)^2+6ab]
=(a+2b)(a-2b)[a^2+4b^2-2ab][a^2+4b^2+2ab]
=(a^2-4b^2)[(a^2+4b^2)^2-4a^2b^2]
=(a^2-4b^2)*(a^2+4b^2)^2-4a^2b^2(a^2-4b^2)
=a^6+4a^4b^2-16a^2b^4-64b^6-4a^4b^2+16a^2b^4
=a^6-64b^6
(a-1)(a^4+a^3+a^2+a+1)＝(a-1)[a^3(a+1)+a(a+1)+1)]
=(a-1)*a^3(a+1)+(a-1)*a(a+1)+a-1
=a^3(a^2-1)+a(a^2-1)+a-1
=a^5-a^3+a^3-a+a-1
=a^5-1
=(a+2b)(a-2b)[a^2+4b^2-2ab][a^2+4b^2+2ab]
=(a^2-4b^2)[(a^2+4b^2)^2-4a^2b^2]
=(a^2-4b^2)*(a^2+4b^2)^2-4a^2b^2(a^2-4b^2)
=a^6+4a^4b^2-16a^2b^4-64b^6-4a^4b^2+16a^2b^4
=a^6-64b^6
(a-1)(a^4+a^3+a^2+a+1)＝(a-1)[a^3(a+1)+a(a+1)+1)]
=(a-1)*a^3(a+1)+(a-1)*a(a+1)+a-1
=a^3(a^2-1)+a(a^2-1)+a-1
=a^5-a^3+a^3-a+a-1
=a^5-1
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