Question
Subtract polynomials: $ \, \color{blue}{ 4y+5y^2-6 } \, $ , $ \, \color{orangered}{ 5y+27-y^2 }$.
Answer
$$ \left( \color{blue}{4y+5y^2-6} \right) - \left( \color{orangered}{5y+27-y^2} \right) = 6y^2-y-33 $$
Explanation
Step 1: First we have to write polynomials in descending order.
$$ \begin{aligned} P(x) &= 5y^2+4y-6 \\ Q(x) &= -y^2+5y+27 \\ \end{aligned} $$Step 2: Write second polynomial below the first one. Making sure like terms are lined up.
$$ \begin{array}{lrrr} & 5y^2 & 4y & -6 \\ \color{red}{ - } & -y^2 & 5y & 27 \\ \hline \end{array} $$Step 3: Change ALL the signs in the second row.
$$ \begin{array}{lrrr} & 5y^2 & 4y & -6 \\ \color{red}{ - } & y^2 & -5y & -27 \\ \hline \end{array} $$Step 4: Combine like terms (add each column):
$$ \begin{array}{lrrr} & 5y^2 & 4y & -6 \\ \color{red}{ - } & y^2 & -5y & -27 \\ \hline & 4y^2 & 9y & 21 \end{array} $$This page was created using
Polynomial Operations Calculator