Question

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

Short answer

The sum of the given polynomials is$5x^2-5xy+5y^2$

Step-by-step solution

Step 1. Given information

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

Step 2. Distribute and identify like terms 

$\begin{array}{l}\text{Wehave}\left(3x^2-4xy+5y^2\right)+\left(2x^2-xy\right)\\ \text{Distributeandidentifyliketermsandthenrearrangetheterms}\\ \Rightarrow \left(3x^2-4xy+5y^2\right)+\left(2x^2-xy\right)=\underset{¯}{3x^2}-\underset{¯}{\underset{¯}{4xy}}+5y^2+\underset{¯}{2x^2}-\underset{¯}{\underset{¯}{xy}}\\ =\left(3+2\right)x^2+\left(-4-1\right)xy+5y^2\\ =5x^2-5xy+5y^2\end{array}$