Subtract polynomials: $ \, \color{blue}{ 3a-4a } \, $ , $ \, \color{orangered}{ 6a-12a }$.

$$ \left( \color{blue}{3a-4a} \right) - \left( \color{orangered}{6a-12a} \right) = 5a $$

Step 1: First we have to write polynomials in descending order.

$$ \begin{aligned} P(x) &= -a \\ Q(x) &= -6a \\ \end{aligned} $$

Step 2: Write second polynomial below the first one. Making sure like terms are lined up.

$$ \begin{array}{lr} & -a \\ \color{red}{ - } & -6a \\ \hline \end{array} $$

Step 3: Change ALL the signs in the second row.

$$ \begin{array}{lr} & -a \\ \color{red}{ - } & 6a \\ \hline \end{array} $$

Step 4: Combine like terms (add each column):

$$ \begin{array}{lr} & -a \\ \color{red}{ - } & 6a \\ \hline & -7a \end{array} $$

Polynomial Operations Calculator