Question
Subtract polynomials: $ \, \color{blue}{ -d+6d^3+4d^2 } \, $ , $ \, \color{orangered}{ 12-4d+5d^2 }$.
Answer
$$ \left( \color{blue}{-d+6d^3+4d^2} \right) - \left( \color{orangered}{12-4d+5d^2} \right) = 6d^3-d^2+3d-12 $$
Explanation
Step 1: First we have to write polynomials in descending order.
$$ \begin{aligned} P(x) &= 6d^3+4d^2-d \\ Q(x) &= 5d^2-4d+12 \\ \end{aligned} $$Step 2: Write second polynomial below the first one. Making sure like terms are lined up.
$$ \begin{array}{lrrrr} & 6d^3 & 4d^2 & -d & \\ \color{red}{ - } & & 5d^2 & -4d & 12 \\ \hline \end{array} $$Step 3: Change ALL the signs in the second row.
$$ \begin{array}{lrrrr} & 6d^3 & 4d^2 & -d & \\ \color{red}{ - } & & -5d^2 & 4d & -12 \\ \hline \end{array} $$Step 4: Combine like terms (add each column):
$$ \begin{array}{lrrrr} & 6d^3 & 4d^2 & -d & \\ \color{red}{ - } & & -5d^2 & 4d & -12 \\ \hline & 6d^3 & 9d^2 & -5d & 12 \end{array} $$This page was created using
Polynomial Operations Calculator