Subtract polynomials: $ \, \color{blue}{ 4v^2+5v^4-7v^3 } \, $ , $ \, \color{orangered}{ 5v^2-5v^4+4v^3 }$.

$$ \left( \color{blue}{4v^2+5v^4-7v^3} \right) - \left( \color{orangered}{5v^2-5v^4+4v^3} \right) = 10v^4-11v^3-v^2 $$

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

$$ \begin{aligned} P(x) &= 5v^4-7v^3+4v^2 \\ Q(x) &= -5v^4+4v^3+5v^2 \\ \end{aligned} $$

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

$$ \begin{array}{lrrr} & 5v^4 & -7v^3 & 4v^2 \\ \color{red}{ - } & -5v^4 & 4v^3 & 5v^2 \\ \hline \end{array} $$

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

$$ \begin{array}{lrrr} & 5v^4 & -7v^3 & 4v^2 \\ \color{red}{ - } & 5v^4 & -4v^3 & -5v^2 \\ \hline \end{array} $$

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

$$ \begin{array}{lrrr} & 5v^4 & -7v^3 & 4v^2 \\ \color{red}{ - } & 5v^4 & -4v^3 & -5v^2 \\ \hline & & -3v^3 & 9v^2 \end{array} $$

Polynomial Operations Calculator