Q. 350 - Intermediate Algebra

Question

In the following exercises, factor by grouping. 

$x^{2}y-x{y}^2+2x-2y$

Step-by-Step Solution

Answer

The factored form of the polynomial is, 

$\left(x-y\right)\left(xy+2\right)$

Step 1. Given Information

We are given a polynomial, 

$x^{2}y-x{y}^2+2x-2y$

Step 2. Factorizing the polynomial

Grouping the terms, we get 

$x^{2}y-x{y}^2+2x-2y=\left(x^{2}y-x{y}^2\right)+\left(2x-2y\right)$

Factoring out GCF, we get

$x^{2}y-x{y}^2+2x-2y=xy\left(x-y\right)+2\left(x-y\right)$

Again factoring out GCF, we get

$x^{2}y-x{y}^2+2x-2y=\left(x-y\right)\left(xy+2\right)$

Step 3. Checking the factorization

 Multiplying the factors, 

$$\begin{gathered} \left(x-y\right)\left(xy+2\right)=x^{2}y-x{y}^2+2x-2y \\ x\left(xy+2\right)-y\left(xy+2\right)=x^{2}y-x{y}^2+2x-2y \\ {x}^{2}y-x{y}^2+2x-2y=x^{2}y-x{y}^2+2x-2y \\ LHS=RHS \end{gathered}$$

Hence the factorization is correct.