Subtract polynomials: $ \, \color{blue}{ 3a^2+1 } \, $ , $ \, \color{orangered}{ 4+2a^2 }$.

$$ \left( \color{blue}{3a^2+1} \right) - \left( \color{orangered}{4+2a^2} \right) = a^2-3 $$

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

$$ \begin{aligned} P(x) &= 3a^2+1 \\ Q(x) &= 2a^2+4 \\ \end{aligned} $$

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

$$ \begin{array}{lrr} & 3a^2 & 1 \\ \color{red}{ - } & 2a^2 & 4 \\ \hline \end{array} $$

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

$$ \begin{array}{lrr} & 3a^2 & 1 \\ \color{red}{ - } & -2a^2 & -4 \\ \hline \end{array} $$

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

$$ \begin{array}{lrr} & 3a^2 & 1 \\ \color{red}{ - } & -2a^2 & -4 \\ \hline & 5a^2 & 5 \end{array} $$

Polynomial Operations Calculator