Subtract polynomials: $ \, \color{blue}{ 10x^2+3 } \, $ , $ \, \color{orangered}{ 9x^2+4+1 }$.

$$ \left( \color{blue}{10x^2+3} \right) - \left( \color{orangered}{9x^2+4+1} \right) = x^2-2 $$

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

$$ \begin{aligned} P(x) &= 10x^2+3 \\ Q(x) &= 9x^2+5 \\ \end{aligned} $$

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

$$ \begin{array}{lrr} & 10x^2 & 3 \\ \color{red}{ - } & 9x^2 & 5 \\ \hline \end{array} $$

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

$$ \begin{array}{lrr} & 10x^2 & 3 \\ \color{red}{ - } & -9x^2 & -5 \\ \hline \end{array} $$

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

$$ \begin{array}{lrr} & 10x^2 & 3 \\ \color{red}{ - } & -9x^2 & -5 \\ \hline & 19x^2 & 8 \end{array} $$

Polynomial Operations Calculator