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二项式与多项式的乘积:回顾

复习如何用多于两项的多项式,如 x^2 - 5x - 6,乘以二项式,如1 + x。
我们已经学会了如何 乘以二项式 例如 left parenthesis, x, plus, 2, right parenthesis, left parenthesis, x, minus, 7, right parenthesis. 这篇课文里, 我们要学习一个稍微难一点的技能: 用多于二项的多项式乘以二项式.

例题

展开并简化.
left parenthesis, 1, plus, x, right parenthesis, left parenthesis, x, squared, minus, 5, x, minus, 6, right parenthesis
应用乘法分配律.
(1+x)(x25x6)=1(x25x6)+x(x25x6)\begin{aligned}&(\blueD{1+x})(x^2-5x-6)\\ \\ =&\blueD{1}(x^2-5x-6)\blueD{+x}(x^2-5x-6)\\ \end{aligned}
再次应用乘法分配律.
equals, start color #11accd, 1, end color #11accd, left parenthesis, x, squared, right parenthesis, plus, start color #11accd, 1, end color #11accd, left parenthesis, minus, 5, x, right parenthesis, plus, start color #11accd, 1, end color #11accd, left parenthesis, minus, 6, right parenthesis, plus, start color #11accd, x, end color #11accd, left parenthesis, x, squared, right parenthesis, plus, start color #11accd, x, end color #11accd, left parenthesis, minus, 5, x, right parenthesis, plus, start color #11accd, x, end color #11accd, left parenthesis, minus, 6, right parenthesis
注意到规律. 我们用第一个二项式中的每一项去乘以第二个三项式中的每一项.
简化.
=x25x6+x35x26x=x34x211x6\begin{aligned} =&x^2-5x-6+x^3-5x^2-6x\\\\ =&x^3-4x^2-11x-6 \end{aligned}
想了解更多二项式乘以多项式的相关内容吗? 点击此视频.
练习
展开并简化.
left parenthesis, c, squared, minus, 6, right parenthesis, left parenthesis, 2, c, squared, plus, 3, c, minus, 1, right parenthesis

想要更多练习么? 请点击 这个练习.