Study Guide

Distributive Property

Distributive Property

This one is insanely important when working with algebraic expressions. The distributive property basically says this:

x(y+z) = xy +xz

and

x(y-z) = xy - xz

However, the distributive property does not work when the variables inside the parentheses are being multiplied or divided.

x(yz) (not equal to sign) xy(xz)

and

x(y/z) (not equal to sign) xy/xz

Let's go through an example very carefully:

4(3x +z)

By applying the distributive property, we can multiply each term inside the parentheses by 4. This is called "distributing."

distribution arrows 4(3x +1)

Since 12x and 4 are not like terms, this is as far as we can go with the problem.

What about subtraction? Let's look at a subtraction problem using two different methods.

-2(7-2x)

Method 1
Leave as Subtraction
Method 2
Add the Negative
distribution arrows -2(7 - 2x)distribution arrows -2(7 + -2x)

Either way, we get the same answer: -14 + 4x. What a relief.