Add $ \, \color{blue}{ x^2-8 } \, $ and $ \, \color{orangered}{ -4x+3x^2-10 }$.

$$ \left( \color{blue}{x^2-8} \right) + \left( \color{orangered}{-4x+3x^2-10} \right) = 4x^2-4x-18 $$

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

$$ \begin{aligned} P(x) &= x^2-8 \\ Q(x) &= 3x^2-4x-10 \\ \end{aligned} $$

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

$$ \begin{array}{lrrr} & x^2 & & -8 \\ \color{blue}{ + } & 3x^2 & -4x & -10 \\ \hline \end{array} $$

Step 3: Combine like terms (add each column):

$$ \begin{array}{lrrr} & x^2 & & -8 \\ \color{blue}{ + } & 3x^2 & -4x & -10 \\ \hline & 4x^2 & -4x & -18 \end{array} $$

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