Question
Subtract polynomials: $ \, \color{blue}{ 3n+n^3-4n^2 } \, $ , $ \, \color{orangered}{ n^2-3n-2n^3+7 }$.
Answer
$$ \left( \color{blue}{3n+n^3-4n^2} \right) - \left( \color{orangered}{n^2-3n-2n^3+7} \right) = 3n^3-5n^2+6n-7 $$
Explanation
Step 1: First we have to write polynomials in descending order.
$$ \begin{aligned} P(x) &= n^3-4n^2+3n \\ Q(x) &= -2n^3+n^2-3n+7 \\ \end{aligned} $$Step 2: Write second polynomial below the first one. Making sure like terms are lined up.
$$ \begin{array}{lrrrr} & n^3 & -4n^2 & 3n & \\ \color{red}{ - } & -2n^3 & n^2 & -3n & 7 \\ \hline \end{array} $$Step 3: Change ALL the signs in the second row.
$$ \begin{array}{lrrrr} & n^3 & -4n^2 & 3n & \\ \color{red}{ - } & 2n^3 & -n^2 & 3n & -7 \\ \hline \end{array} $$Step 4: Combine like terms (add each column):
$$ \begin{array}{lrrrr} & n^3 & -4n^2 & 3n & \\ \color{red}{ - } & 2n^3 & -n^2 & 3n & -7 \\ \hline & -n^3 & -3n^2 & & 7 \end{array} $$This page was created using
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