Add $ \, \color{blue}{ 2x^7+24x+3x^2+2x } \, $ and $ \, \color{orangered}{ 3x^7+5x^6+2x^2+6x }$.

$$ \left( \color{blue}{2x^7+24x+3x^2+2x} \right) + \left( \color{orangered}{3x^7+5x^6+2x^2+6x} \right) = 5x^7+5x^6+5x^2+32x $$

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

$$ \begin{aligned} P(x) &= 2x^7+3x^2+26x \\ Q(x) &= 3x^7+5x^6+2x^2+6x \\ \end{aligned} $$

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

$$ \begin{array}{lrrrr} & 2x^7 & & 3x^2 & 26x \\ \color{blue}{ + } & 3x^7 & 5x^6 & 2x^2 & 6x \\ \hline \end{array} $$

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

$$ \begin{array}{lrrrr} & 2x^7 & & 3x^2 & 26x \\ \color{blue}{ + } & 3x^7 & 5x^6 & 2x^2 & 6x \\ \hline & 5x^7 & 5x^6 & 5x^2 & 32x \end{array} $$

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