Combining Like Terms

A coefficient is the number part of a term that includes a variable.

Example: 2x

2 is the coefficient x is the variable

Coefficient

4x + 8x +1

Coefficients are 4 and 8

Constant term

4x and 8x are like terms

like terms: terms with the same variable or variables, raised to the same power.

Like terms can be combined by adding their coefficients.

Example: What do you get when you add the fruit shown?

Combine like terms

+ – +By combining apples with apples and oranges with oranges, you get...

+

1 apple

3 apples + 2 oranges – 2 apples + 2 oranges

+ 4 oranges

coefficients

What’s the “same” term mean? ◦If numbers have a variable, then you can combine only ones that have the same variable

◦You can also combine numbers that have no variables

Only combine terms that are exactly the same!!

Which numbers are the “same”?

5x, 8y, 9z, 10, 12x, 14z, 7

Same: 5x and 12xSame: 10 and 7Same: 9z and 14zSame: 8y

Examples

Terms in an algebraic expression are separated by addition or subtraction signs.

How many terms are in this expression?

The sign in front of each coefficient goes with that term.

Find the like terms, combine their coefficients...

2x + 3y + 5x + 6y + 12

7x + 9y + 12

Example: Simplify 3x – 3y – 8x – yThis is the same as 3x – 3y – 8x – 1y

= – 5x – 4y

Example: Simplify 2x + 3y + 5x + 6y + 12

Example:

Reorder the terms.

Combine like terms.

Combine like terms.

Identify like terms.

Combine coefficients: 14 – 5 = 9

A. 14a – 5a

9a

B. 7y + 8 – 3y – 1 + y Identify like terms ; the coefficient of y is 1, because 1y = y.

5y + 7 Combine coefficients:

7 – 3 + 1 = 5 and 8 – 1 = 7

Combine like terms.Identify like terms; the coefficient of q is 1, because 1q = q.

Combine coefficients: 4 – 1 = 3

Identify like terms; the coefficient of c is 1, because 1c = c.

6

3q

C. 4q – q

D. 5c + 8 – 4c – 2 – c

Combine coefficients:

5 – 4 – 1 = 0 and 8 – 2 = 6

E. 4m + 9n – 2

4m + 9n – 2

Combine like terms.

No like terms.

F. 5m – 7m – 8 + 4

-2m – 4

Remember, to simplify an expression means to perform all possible operations, including combining like terms.

In other words, simplify means solve!

1. 4x + 5y – 2x + 3y 2. 5x + 5y + 2x + 2y

3. 3 + 5x – 4y + 2y – 8x

Final Problems:

2x + 8y

7x + 7y

3 – 3x – 2y

Practice:worksheet