Question

In the following exercises, add the polynomials.

$\left(5y^2+12y+4\right)+\left(6y^2-8y+7\right)$

Short answer

The sum of the polynomials is$11y^2+4y+11.$

Step-by-step solution

Step 1. Given information

$\begin{array}{l}\text{Thegivenexpressionis}\\ \left(5y^2+12y+4\right)+\left(6y^2-8y+7\right)\\ \text{Wehavetoaddthepolynomials.}\end{array}$

Step 2. Add the polynomials

$\begin{array}{l}\Rightarrow \left(5y^2+12y+4\right)+\left(6y^2-8y+7\right)\\ =5y^2+12y+4+6y^2-8y+7\left[\text{Rewritewithouttheparenthese}\right]\\ =5y^2+6y^2+12y-8y+4+7\left[\text{Combinetheliketerms}\right]\\ =\left(5+6\right)y^2+\left(12-8\right)y+11\\ =11y^2+4y+11\end{array}$