Question

# Add: $2x\left(z-x-y\right)and2y\left(z-y-x\right)$

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Solution

## To add : $2x\left(z-x-y\right)and2y\left(z-y-x\right)$Firstly we will multiply the common term with the brackets given, and then add the like terms with one another, we have$\begin{array}{rcl}& =& 2x\left(z–x–y\right)+2y\left(z–y–x\right)\\ & =& \left(2x×z\right)–\left(2x×x\right)–\left(2x×y\right)+\left(2y×z\right)–\left(2y×y\right)–\left(2y×x\right)\\ & =& 2xz–2{x}^{2}–2xy+2yz–2{y}^{2}–2yx\\ & =& 2xz–4xy+2yz–2{x}^{2}–2{y}^{2}\end{array}$Hence, On adding $2x\left(z-x-y\right)and2y\left(z-y-x\right)$ , we get $2xz-4xy+2yz-2{x}^{2}-2{y}^{2}$.

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