Question
Subtract polynomials: $ \, \color{blue}{ 12x^5+4x^4+9x^3-10x^2+15 } \, $ , $ \, \color{orangered}{ 24x^5+9x^3-7x^2+8 }$.
Answer
$$ \left( \color{blue}{12x^5+4x^4+9x^3-10x^2+15} \right) - \left( \color{orangered}{24x^5+9x^3-7x^2+8} \right) = -12x^5+4x^4-3x^2+7 $$
Explanation
Step 1: Write second polynomial below the first one. Making sure like terms are lined up.
$$ \begin{array}{lrrrrr} & 12x^5 & 4x^4 & 9x^3 & -10x^2 & 15 \\ \color{red}{ - } & 24x^5 & & 9x^3 & -7x^2 & 8 \\ \hline \end{array} $$Step 2: Change ALL the signs in the second row.
$$ \begin{array}{lrrrrr} & 12x^5 & 4x^4 & 9x^3 & -10x^2 & 15 \\ \color{red}{ - } & -24x^5 & & -9x^3 & 7x^2 & -8 \\ \hline \end{array} $$Step 3: Combine like terms (add each column):
$$ \begin{array}{lrrrrr} & 12x^5 & 4x^4 & 9x^3 & -10x^2 & 15 \\ \color{red}{ - } & -24x^5 & & -9x^3 & 7x^2 & -8 \\ \hline & 36x^5 & 4x^4 & 18x^3 & -17x^2 & 23 \end{array} $$This page was created using
Polynomial Operations Calculator