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Basic Algebra

Basic Algebra

At a Glance - Distributive Property

Let's review the properties using variables instead of numbers:

Commutative x + y = y + x xy = yx
Associative x + (y +z) = (x + y) + z x(yz) = (xy)z
Inverse x + -x = 0 x(1/x) = 1
Identity x + 0 = x x(1) =x

The properties above do NOT work with subtraction and division.

Here's a handy visual aid on reviewing the properties:

Distributive Property

This one is very important when working with algebraic expressions. It basically says this:

x(y+z) = xy +xz


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)


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.

Well, what about subtraction? Let's look at a subtraction problem using two different methods.


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

Exercise 1

Use the distributive property to simplify 5(6y + -1)

Exercise 2

Use the distributive property to simplify -3(2z - 4)