Simplifying Algebraic Expressions Adapted by Mrs. Garay

Simplify  20      5 + 3

Learn to combine like terms in an expression.

Vocabulary terms like terms equivalent expressions simplify

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. Equivalent expressions have the same value for all values of the variables. Constants such as 4, 0.75, and 11 are like terms because none of them have a variable. Helpful Hint

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

Combine like terms. Example 1: Combining Like Terms To Simplify Identify like terms. Combine coefficients: 14 – 5 = 9 A. 14a – 5a 9a9a B. 7y – 3y 2 – 1 + y Identify like terms; the coefficient of y is 1, because 1y = y. Combine coefficients: 7 – 3 = 4 and 8 – 1 = 7 4y 2 + y + 7

Combine like terms. Now you try! 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. Combine coefficients: 5 – 4 – 1 = 0 and 8 – 2 = 6 6 3q3q A. 4q – q B. 5c + 8 – 4c – 2 – c

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

Combine like terms. Example 2B: Combining Like Terms in Two-Variable Expressions No like terms. 4m 3 + 9n – 2

Combine like terms. Your turn again! Identify like terms. Combine coefficients. A. 2x + 5x – 4y + 3 7x – 4y + 3 2x + 5x – 4y + 3 Identify like terms. Combine coefficients. B. 9d + 7c – 4d – 2c 5d + 5c 9d + 7c – 4d – 2c No like terms. C. 8g + c – 6 8g + c – 6

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!

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

Simplify 3(c + 7) – c. Your turn! Distributive Property. Multiply. 3(c + 7) – c 3c + 21 – c 3(c) + 3(7) – c 2c + 21 Combine coefficients: 3 – 1 = 2.

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

Solve 7c – c = 102. Your turn! Identify like terms. The coefficient of c is 1. Combine coefficients: 7 – 1 = 6 7c – c = 102 6c = 102 c = 17 Divide both sides by

Now lets see what you can do! You will be combining like terms by answering questions from a power point! Good Luck!