Chapter 7.5, Problem 53HP

To determine

Explain how the GCF is used to factor an expression. Use the term Distributive Property in your response.

Explanation of Solution

Concept Used:

GCF is used to factor an expression to show the expression in its simplest form. When using the GCF of the expression, it is somewhat expanding the expression using the distributive property.

The Distributive property states that multiply each term inside the parentheses by the number outside the parentheses. So the term outside the parenthesis is the GCF of the expression.

Finding the common factor allows us to apply the Distributive Property to the statement.

The Distributive Property applies multiplication to an existing addition statement. It means that a number outside the parentheses of an addition problem can be multiplied by each number inside the parentheses. Or in the opposite case, a common factor can be factored out and written outside the parentheses.

So, with 3 as our common factor, the statement $3x+3y$ becomes $3(x+y)$ , or 3 multiplied by $(x+y)$

You can always check your work by multiplying the numbers in your answer.

For $3(x+y)$ , you can check your work as follows: $3(x+y)=3·x+3·y=3x+3y$