# Distributive Property

The Distributive Property allows you to distribute the multiplying of one number times each term within a quantity.

An example is the easiest way to see how it works:

4(5x + 3)

To distribute, we will multiply the 4 times each term (5x and 3) inside the parentheses. That will turn this multiplication problem into an addition problem.

4(5x + 3)

4(5x) + 4(3) *Note how we keep the + sign between the terms.

Now multiply each term out:

20x + 12

When multiplying with the distributive property, you must keep in mind all the rules for multiplying with variables and with exponents.

Here are a few more examples:

1. 5(7a – 6) = 5(7a) – 5(6) = 35a – 30
2. 4(1/2 + 4a) = 4(1/2) + 4(4a) = 2 + 16a
3. 1/3(6a – 9b) = 1/3(6a) – 1/3(9b) = 2a – 3b
4. 5a(2a + 8b) = 5a(2a) + 5a(8b) = 10a2 + 40ab
5. 7a(3ac – x/14) = 7a(3ac) – 7a(x/14) = 21a2c – ax/2
6. x2(y – 2x) = x2(y) – x2(2x) = x2y – 2×3
7. 4y(7x + y – 5) = 4y(7x) + 4y(y) – 4y(5) = 28xy + 16y2 – 20y
8. 3x(9x – 2z + 1) = 3x(9x) – 3x(2z) + 3x(1) = 27×2 – 6xz + 3x