Combine Like TermsCombine Like TermsCombine Like TermsCombine Like TermsI can simplify expressions with I can simplify expressions with

several variables by combining like several variables by combining like terms.terms.

VocabularyVocabulary

ConstantConstantA number with nothing else A number with nothing else

attached to it. attached to it.

Examples: 1, 2, 47, 925Examples: 1, 2, 47, 925

VocabularyVocabulary

VariableVariable

A letter that represents an unknown A letter that represents an unknown number. number.

Examples: a, b, x, y Examples: a, b, x, y

VocabularyVocabulary

CoefficientCoefficient

The number in front of the variable. The number in front of the variable.

Examples: 3x 3 is the coefficientExamples: 3x 3 is the coefficient

2x 2 is the coefficient 2x 2 is the coefficient

Like Terms:– In an expression, like terms are

the terms that have the same variables, raised to the same powers (same exponents).•Examples: 4x and -3x or 2y2 and –y2

• Like terms because each term consists of a single variable, x, and a numeric coefficient: 2x, 45x, x, 0x, -26x, -x

• Like terms because they are all constants: 15, -2, 27, 9043, 0.6

• Like terms because they are all y² with a coefficient: 3y², y², -y², 26y²

What are unlike terms?

• The following two terms both have a single variable, but the terms are not alike since different variables are used: 17x, 17z

• Each y variable in the terms below has a different exponent, therefore these are unlike terms: 15y, 19y², 31y5

• Although both terms below have an x variable, only one term has the y variable, thus these are not like terms either: 19x, 14xy

Combine Like TermsCombine Like TermsCombine Like TermsCombine Like TermsI can simplify expressions with I can simplify expressions with

several variables by combining like several variables by combining like terms.terms.

Like Terms – same variable with same exponent

6x + 2x =When combining like terms, only use the coefficients.

6x + 2x = 8x

4x + 3y – 2x + 4y =Simplify

2x + 7y

Simplify

Never, NEVER, combine x’s and y’s or constant terms with variable terms. 2x + 7y ≠ 9xy and 3a + 6 ≠ 9a.

Key Skills

5 cats + 3 cats5 cats + 3 cats

8 cats8 cats

5a + 3a5a + 3a

8a8a

5 apples + 3 oranges5 apples + 3 oranges

5 apples + 3 5 apples + 3 orangesoranges

5 cats + 3 dogs5 cats + 3 dogs

5 cats + 3 dogs5 cats + 3 dogs

You Try• 3y + 2 + 3x – y + 5x • x + x

Distribute by multiplication:Distribute by multiplication:

15n and 20 are not alike and therefore cannot be combined. The answer 15n + 20 is simplified because we do not know what the value of n is at this time and cannot

complete the multiplication part of this problem.

15n and 20 are not alike and therefore cannot be combined. The answer 15n + 20 is simplified because we do not know what the value of n is at this time and cannot

complete the multiplication part of this problem.

)43(5 n )3(5 n

)4(5

n15 20

The Distributive Property

• Expressions with variables:

Simplify 5(3n + 4).• No symbol between the 5 and the parenthesis

indicates a multiplication problem.

The constant terms 8 and 6 can be combined to form the constant number 14. The answer 28n + 14 is simplified because we do not know what the value of n is at

this time and cannot complete the multiplication part of this problem.

The constant terms 8 and 6 can be combined to form the constant number 14. The answer 28n + 14 is simplified because we do not know what the value of n is at

this time and cannot complete the multiplication part of this problem.

6)27(4 n )7(4 n

)2(4

n28 8

6

6

n28 14

The Distributive Property

• Simplify 4(7n + 2) + 6.• No symbol between the 4 and the

parenthesis indicates a multiplication problem.

Step 1) Use the Distributive Property 3 (2x – 5) - 2x

Step 2) Combine Like Terms 6x – 15 – 2x *** 6x and 2x are like terms!!!!

Step 3) Simplified Expression 4x – 15

Distributive Property

Distributive PropertyExample:

6(a + 3) Use the Distributive

Property

(6a) + (6 x 3) Multiply

6a + 18 Simplified

***CAN NOT add 6a + 18 together because they are not like terms.

Solve: 2x + 6(x + 1)

Explain how each of the below answers are wrong and why.

• 2x + 6x + 1• 9x

Practice Problems