Question
Subtract polynomials: $ \, \color{blue}{ b^4-b^3-7b^2+6 } \, $ , $ \, \color{orangered}{ 8b^4+3+5b-3b^2 }$.
Answer
$$ \left( \color{blue}{b^4-b^3-7b^2+6} \right) - \left( \color{orangered}{8b^4+3+5b-3b^2} \right) = -7b^4-b^3-4b^2-5b+3 $$
Explanation
Step 1: First we have to write polynomials in descending order.
$$ \begin{aligned} P(x) &= b^4-b^3-7b^2+6 \\ Q(x) &= 8b^4-3b^2+5b+3 \\ \end{aligned} $$Step 2: Write second polynomial below the first one. Making sure like terms are lined up.
$$ \begin{array}{lrrrrr} & b^4 & -b^3 & -7b^2 & & 6 \\ \color{red}{ - } & 8b^4 & & -3b^2 & 5b & 3 \\ \hline \end{array} $$Step 3: Change ALL the signs in the second row.
$$ \begin{array}{lrrrrr} & b^4 & -b^3 & -7b^2 & & 6 \\ \color{red}{ - } & -8b^4 & & 3b^2 & -5b & -3 \\ \hline \end{array} $$Step 4: Combine like terms (add each column):
$$ \begin{array}{lrrrrr} & b^4 & -b^3 & -7b^2 & & 6 \\ \color{red}{ - } & -8b^4 & & 3b^2 & -5b & -3 \\ \hline & 9b^4 & -b^3 & -10b^2 & 5b & 9 \end{array} $$This page was created using
Polynomial Operations Calculator