Using Distributive Property to Factor Variable Expressions

The distributive property is a mathematical rule that states that multiplying a single value by a sum of values is the same as multiplying each individual value in the sum by that single value and then adding the products.

A step-by-step guide to identifying equivalent expressions

The distributive property can also be used to factor in variable expressions.

To factor variable expressions utilizing the distributive property, follow these steps:
Step 1: Multiply or distribute the outer term to the inner terms.
Step 2: Then, combine the like terms.
Step 3: Write terms in a way that the constants and variables are on the opposite sides of the equal’s sign.
Step 4: Finally, resolve the equation and simplify.

Using Distributive Property to Factor Variable Expressions – Example 1

Factor the expression, \(8p+16\)t. Write a product with a whole number greater than 1.
Solution:
Step 1: Find the greatest common factor of 8p and 16t. It is 8.
Step 2: Divide each number by 8. \(8÷8=1, 16÷8=2\)
Step 3: Use the distributive property to write an equivalent expression.
\(8p+16t=8×p+8×2t=8(p+2t)\)

Using Distributive Property to Factor Variable Expressions – Example 2

Factor the expression, \(70+30n\). Write a product with a whole number greater than 1.
Step 1: Find the greatest common factor of 70 and 30n. It is 10.
Step 2: Divide each number by \(10. 70÷10=7, 30÷10=3\)
Step 3: Use the distributive property to write an equivalent expression.
\(70+30n=10×7+10×3n=10(7+3n)\)