Subtract polynomials: $ \, \color{blue}{ 10x^2-4+3 } \, $ , $ \, \color{orangered}{ 7x^2-3x+13 }$.

$$ \left( \color{blue}{10x^2-4+3} \right) - \left( \color{orangered}{7x^2-3x+13} \right) = 3x^2+3x-14 $$

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

$$ \begin{aligned} P(x) &= 10x^2-1 \\ Q(x) &= 7x^2-3x+13 \\ \end{aligned} $$

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

$$ \begin{array}{lrrr} & 10x^2 & & -1 \\ \color{red}{ - } & 7x^2 & -3x & 13 \\ \hline \end{array} $$

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

$$ \begin{array}{lrrr} & 10x^2 & & -1 \\ \color{red}{ - } & -7x^2 & 3x & -13 \\ \hline \end{array} $$

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

$$ \begin{array}{lrrr} & 10x^2 & & -1 \\ \color{red}{ - } & -7x^2 & 3x & -13 \\ \hline & 17x^2 & -3x & 12 \end{array} $$

Polynomial Operations Calculator