Question

$\text{Find the sum:}\left(7x^2-4x+5\right)+\left(x^2-7x+3\right)$

Short answer

The sum of the polynomials is$8x^2-11x+8$

Step-by-step solution

Step 1. Given information 

$\begin{array}{l}\text{Thegivenpolynomialexpressionis}\\ \left(7x^2-4x+5\right)+\left(x^2-7x+3\right)\\ \text{Wehavetofindthesum}\end{array}$

Step 2. Identify the like terms and rewrite the expression

$\begin{array}{l}\text{Wehave}\left(7x^2-4x+5\right)+\left(x^2-7x+3\right)\\ \text{Rewritewithouttheparentheses,rearrangingtogettheliketermstogether}\\ \Rightarrow \left(7x^2-4x+5\right)+\left(x^2-7x+3\right)=7x^2+x^2-4x-7x+3+5\end{array}$

Step 3. Operate the like terms

$\begin{array}{l}\Rightarrow \left(7x^2-4x+5\right)+\left(x^2-7x+3\right)=7x^2+x^2-4x-7x+3+5\\ =\left(7+1\right)x^2-\left(4+7\right)x+8\\ =8x^2-11x+8\end{array}$