Distributive Property Equations

Front

What is the Distributive Property?

Back

The Distributive Property states that a(b + c) = ab + ac. It allows you to multiply a single term by two or more terms inside a set of parentheses.

Front

How do you apply the Distributive Property to the expression 3(x + 4)?

Back

3(x + 4) = 3x + 12.

Front

What is an example of using the Distributive Property with subtraction?

Back

For the expression 5(y - 2), it becomes 5y - 10.

Front

If you have the equation 2(3 + x) = 14, how do you solve for x?

Back

First, apply the Distributive Property: 6 + 2x = 14. Then, subtract 6 from both sides: 2x = 8. Finally, divide by 2: x = 4.

Front

What does it mean to factor an expression using the Distributive Property?

Back

Factoring using the Distributive Property means rewriting an expression as a product of its factors, such as turning 6x + 12 into 6(x + 2).

Front

Can you give an example of a real-world application of the Distributive Property?

Back

If a box contains 4 packs of pencils, each with 5 pencils, you can calculate the total number of pencils as 4(5) = 20.

Front

What is the result of applying the Distributive Property to 7(2 + 3)?

Back

7(2 + 3) = 7*2 + 7*3 = 14 + 21 = 35.

Front

How do you simplify the expression 4(2x + 3y) using the Distributive Property?

Back

4(2x + 3y) = 8x + 12y.

Front

What is the Distributive Property used for in algebra?

Back

It is used to simplify expressions and solve equations by distributing a multiplier across terms in parentheses.

Front

If you have the expression 10 - 2(3 + x), how do you simplify it?

Back

10 - 2(3 + x) = 10 - 6 - 2x = 4 - 2x.