1. Warm Up
Simplify.
 5 + 3 20
2. 16   1 11  8
 20  2 3

2. Learn to combine like terms in an expression.

3. Vocabulary
terms
like terms
equivalent expressions
simplify

4. Terms in an expression are separated by plus or minus signs.
Like terms can be grouped together because they have the same variable raised to the same exponents.
Constants such as 4, 0.75, and 11 are like terms because none of them have a variable.
Helpful Hint
Equivalent expressions have the same value for all values of the variables.

5. To simplify an expression, perform all possible operations, including combining like terms.

6. Additional Example 1: Combining Like Terms To Simplify
Combine like terms.
A. 14a – 5a
Identify like terms. 9a
Combine coefficients: 14 – 5 = 9
Identify like terms; the coefficient of y is 1, because 1y = y.
B. 7y2 + 8 – 3y2 – 1 + y
Combine coefficients: 7 – 3 = 4 and 8 – 1 = 7
4y2 + y + 7

7. Additional Example 2A: Combining Like Terms in Two-Variables Expressions
Combine like terms.
5t2 + 7p – 3p – 2t2
5t2 + 7p – 3p – 2t2
Identify like terms.
3t2 + 4p
Combine coefficients.

8. Additional Example 2B: Combining Like Terms in Two-Variable Expressions
Combine like terms.
4m3 + 9n – 2
4m3 + 9n – 2
No like terms.

9. The Distributive Property states that a(b + c) = ab + ac for all real numbers a, b, and c. For example, 2(3 + 5) = 2(3) + 2(5).
Remember!

10. Additional Example 3: Using the Distributive Property to Simplify
Simplify 6(5 + n) – 2n.
6(5 + n) – 2n
6(5) + 6(n) – 2n
Distributive Property.
30 + 6n – 2n
Multiply.
30 + 4n
Combine coefficients: 6 – 2 = 4.

11. Additional Example 4: Combining Like Terms to Solve Algebraic Equations
Solve x + 3x = 48.
x + 3x = 48
Identify like terms. The coefficient of x is 1.
4x = 48
Combine coefficients: = 4
4x = 48
Divide both sides by 4. 4 4
x = 12