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

$$ \left( \color{blue}{a-2a^2} \right) - \left( \color{orangered}{3a^2-4a^3} \right) = 4a^3-5a^2+a $$

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

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

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

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

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

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

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

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

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