問題の解答
検索用コード（LaTeX）
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% 例題I1.1.2：多項式の加法・減法（One More）★★
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$A=x^2+3x-1$，$B=2x^2-2x+5$について，次の式を計算せよ．
(1) $A+B$
(2) $A-B$
(3) $2A+B$
(4) $2(3A-B)-\{(2A+3B)-(A+2B)\}$
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% 例題I1.1.2の解答（One More）★★
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(1)
\begin{align*}
A+B&=(x^2+3x-1)+(2x^2-2x+5)\\
&=(x^2+2x^2)+(3x-2x)+(-1+5)\\
&=3x^2+x+4
\end{align*}
(2)
\begin{align*}
A-B&=(x^2+3x-1)-(2x^2-2x+5)\\
&=x^2+3x-1-2x^2+2x-5\\
&=(x^2-2x^2)+(3x+2x)+(-1-5)\\
&=-x^2+5x-6
\end{align*}
(3)
\begin{align*}
2A+B&=2(x^2+3x-1)+(2x^2-2x+5)\\
&=2x^2+6x-2+2x^2-2x+5\\
&=(2x^2+2x^2)+(6x-2x)+(-2+5)\\
&=4x^2+4x+3
\end{align*}
(4)
\begin{align*}
&2(3A-B)-\{(2A+3B)-(A+2B)\}=2(3A-B)-(A+B)\\
=&6A-2B-A-B\\
=&5A-3B\\
=&5(x^2+3x-1)-3(2x^2-2x+5)\\
=&5x^2+15x-5-6x^2+6x-15\\
=&-x^2+21x-20
\end{align*}
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% 問題I1.1.2：多項式の加法・減法（One More）★★
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$A=2x^2-4x+3$，$B=3x^2+x-7$について，次の式を計算せよ．
(1) $A+B$
(2) $A-B$
(3) $3A-2B$
(4) $4(A+B)-(2A-3B)$
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% 問題I1.1.2の解答（One More）★★
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(1)
\begin{align*}
A+B&=(2x^2-4x+3)+(3x^2+x-7)\\
&=(2x^2+3x^2)+(-4x+x)+(3-7)\\
&=5x^2-3x-4
\end{align*}
(2)
\begin{align*}
A-B&=(2x^2-4x+3)-(3x^2+x-7)\\
&=2x^2-4x+3-3x^2-x+7\\
&=(2x^2-3x^2)+(-4x-x)+(3+7)\\
&=-x^2-5x+10
\end{align*}
(3)
\begin{align*}
3A-2B&=3(2x^2-4x+3)-2(3x^2+x-7)\\
&=6x^2-12x+9-6x^2-2x+14\\
&=(6x^2-6x^2)+(-12x-2x)+(9+14)\\
&=-14x+23
\end{align*}
(4)
\begin{align*}
&4(A+B)-(2A-3B)\\
=&4A+4B-2A+3B\\
=&2A+7B\\
=&2(2x^2-4x+3)+7(3x^2+x-7)\\
=&4x^2-8x+6+21x^2+7x-49\\
=&25x^2-x-43
\end{align*}
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