Distributive Property

Question 1

What is the Distributive Property?

Answer 1

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

Question 2

Give an example of the Distributive Property.

Answer 2

For example, 3(4 + 5) = 3 * 4 + 3 * 5, which simplifies to 12 + 15 = 27.

Question 3

Can you use the Distributive Property with subtraction?

Answer 3

Yes! For example, 2(6 - 3) = 2 * 6 - 2 * 3, which simplifies to 12 - 6 = 6.

Question 4

How does the Distributive Property apply to variables?

Answer 4

If you have 5(x + 2), you can distribute to get 5x + 10.

Question 5

What is the reverse of the Distributive Property?

Answer 5

The reverse is combining like terms; for example, from 6x + 12, you can factor it back to 6(x + 2).

Question 6

Why is the Distributive Property useful?

Answer 6

It simplifies expressions and solves equations more easily by breaking down complex calculations.

Question 7

What are some common mistakes with the Distributive Property?

Answer 7

A common mistake is forgetting to multiply every term in the parentheses or misapplying the signs.

Question 8

How can you check your work when using the Distributive Property?

Answer 8

You can re-combine terms after distribution and see if you get back to the original equation or expression.