Combining Like Terms and Distributive Property

Basic Information a. When you are combining like terms, find terms with common variables ( The Same Variable with the Same Exponents) b. Add The Coefficients (the number in front of the variables) c. Make sure you use The Distributive Property to get rid of any parenthesis before combining like terms

Let’s try to pick out the “like terms

4x and -2x are like terms because they both have an x.

8xy and -7xy are like terms because they both have an xy.

3y2 and 5y2 are like terms because they both have an y2.

2y and y are like terms because they both have a y.

Let’s take a look at an example problem. Combining Like Terms Let’s take a look at an example problem. Both -5x2 and 10x2 have x2 , they are like terms (same variable and same exponents)

Let’s take a look at an example problem. Combining Like Terms Let’s take a look at an example problem. Both 3x and -4x have x , they are like terms (same variable and same exponents)

Combining Like Terms Let’s take a look at an example problem. Both 2 and -8 are numbers, they are like terms.

Let’s take a look at an example problem. Combining Like Terms Let’s take a look at an example problem. Now order all the like terms from the height exponent to the lowest, and last numbers.

Let’s take a look at an example problem. Combining Like Terms Let’s take a look at an example problem. -5x2 and 10x2 comes first

+ Combining Like Terms Let’s take a look at an example problem. Now 3x and -4x comes second Since 3x is positive we write and adding sing in front of it

+ Combining Like Terms Let’s take a look at an example problem. Now numbers +2 and -8 comes last. They are like terms because the are numbers (Constant)

+ Combining Like Terms Let’s take a look at an example problem. Now Combine like terms and Simplify

Let’s take a look at an example problem. Combining Like Terms Let’s take a look at an example problem. + 5 x2 -5x2 + 10x2 = 5x2

Let’s take a look at an example problem. Combining Like Terms Let’s take a look at an example problem. + 5 x2 - 1 x + 3 x – 4 x = - 1 x

+ 5 x2 - 1 x Combining Like Terms Let’s take a look at an example problem. + 5 x2 - 1 x Remember there is no need to put the 1 in front of the variable

+ 5 x2 - 1 x Combining Like Terms Let’s take a look at an example problem. + 5 x2 - 1 x Remember there is no need to put the 1 in front of the variable

Let’s take a look at an example problem. Combining Like Terms Let’s take a look at an example problem. + 5 x2 - x - 6 2 - 8= -6

+ 5 x2 - x - 6 Combining Like Terms The Simplified Equations is Let’s take a look at an example problem. + 5 x2 - x - 6 The Simplified Equations is 5x2 – x – 6

Distributive Property The distributive property is used to simplify expressions with parenthesis. You multiply the term on the outside of the parenthesis by each term on the inside of the parenthesis.

Distributive Property For this problem, you need to multiply 3 by each term on the inside of the parenthesis. You will use this same method for each set of parenthesis in an expression or equation.

Distributive Property Take each set of parenthesis separately and then combine like terms to find the simplified expression.

Distributive Property Take each set of parenthesis separately and then combine like terms to find the simplified expression. 2x + 14

Distributive Property If you have an expression with just a negative sign in front of the parenthesis, assume it is -1 and distribute.

Follow-Up Questions Answer the following questions on loose leaf and hand them in to your teacher.

Follow-Up Questions 1. 2. 3. 4. 5.

Follow-Up Questions 6. 7. 8. 9. 10.