Chapter 13, Problem 1RE

To determine

To factor: The expression $5x+5y$ by removing the greatest common factor.

Answer to Problem 1RE

The expression $5x+5y$ can be factored as $\underset{\_}{5\left(x+y\right)}$.

Explanation of Solution

Procedure used:

To factor an expression containing a common factor:

“1. Find the greatest factor common to each term of the expression.

2. Divide each term by the common factor. Divide mentally if practical.

3. Rewrite the expression as the indicated product of the greatest common factor and the quotient in Step 2”.

Result used:

Distributive property:

For any real number a, x and y, $a\left(x+y\right)=ax+ay$.

Calculation:

The given expression is $5x+5y$.

It is observed that, 5 is a common factor in each term of the exprerssion, so the greatest common factor is 5.

Divide each term in the expression by 5.

$5x+5y=\frac{5x}{5}+\frac{5y}{5}$

Rewrite the given expression as the product of the factor 5 and the sum $\frac{5x}{5}+\frac{5y}{5}$.

$5x+5y=5\left(\frac{5x}{5}+\frac{5y}{5}\right)$

On further simplfications,

$5x+5y=5\left(x+y\right)$

Therefore, the expression $5x+5y$ can be factored as $\underset{\_}{5\left(x+y\right)}$.