Q. 349 - Intermediate Algebra

Question

In the following exercises, factor by grouping.

$ax-ay+bx-by$

Step-by-Step Solution

Answer

 The factored form of the polynomial is, 

$\left(x-y\right)\left(a+b\right)$

Step 1. Given Information

 We are given a polynomial,

$ax-ay+bx-by$

Step 2. Factorizing the polynomial

Grouping the terms, we get

$ax-ay+bx-by=\left(ax-ay\right)+\left(bx-by\right)$

Factoring out greatest common factor, we get

$ax-ay+bx-by=a\left(x-y\right)+b\left(x-y\right)$

Now, again factoring out greatest common factor, we get 

$ax-ay+bx-by=\left(x-y\right)\left(a+b\right)$

Step 3. Checking the factorization

Multiplying the factors, 

$$\begin{gathered} \left(x-y\right)\left(a+b\right)=ax-ay+bx-by \\ a(x-y)+b(x-y)=ax-ay+bx-by \\ ax-ay+bx-by=ax-ay+bx-by \\ LHS=RHS \end{gathered}$$

Hence the factorization is correct.