1-6 Combining Like Terms Learn to combine like terms in an expression. Pre-Algebra 1-6 Combining Like Terms Learn to combine like terms in an expression.

Pre-Algebra 1-6 Combining Like Terms 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 power. Equivalent expressions have the same value for all values of the variables.

Example 1: Combining Like Terms To Simplify Pre-Algebra 1-6 Combining Like Terms 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. 7y + 8 – 3y – 1 + y Combine coefficients: 7 – 3 + 1 = 5 and 8 – 1 = 7 5y + 7

Example 2A: Combining Like Terms in Two-Variables Expressions Pre-Algebra 1-6 Combining Like Terms Example 2A: Combining Like Terms in Two-Variables Expressions Combine like terms. A. 9x + 3y – 2x + 5 9x + 3y – 2x + 5 Identify like terms. 7x + 3y + 5 Combine coefficients: 9 – 2 = 7

Example 2B: Combining Like Terms in Two-Variable Expressions Pre-Algebra 1-6 Combining Like Terms Example 2B: Combining Like Terms in Two-Variable Expressions Combine like terms. B. 5t + 7p – 3p – 2t 5t + 7p – 3p – 2t Identify like terms. Combine coefficients: 5 – 2 = 3 and 7 – 3= 4 3t + 4p

Example 2C: Combining Like Terms in Two-Variable Expressions Pre-Algebra 1-6 Combining Like Terms Example 2C: Combining Like Terms in Two-Variable Expressions Combine like terms. C. 4m + 9n – 2 4m + 9n – 2 No like terms.

Pre-Algebra 1-6 Combining Like Terms 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 power. Equivalent expressions have the same value for all values of the variables.

1-6 Combining Like Terms Try This: Example 1 Combine like terms. Pre-Algebra 1-6 Combining Like Terms Try This: Example 1 Combine like terms. Identify like terms; the coefficient of q is 1, because 1q = q. A. 4q – q 3q Combine coefficients: 4 – 1 = 3 Identify like terms; the coefficient of c is 1, because 1c = c. B. 5c + 8 – 4c – 2 – c Combine coefficients: 5 – 4 – 1 = 0 and 8 – 2 = 6 6

1-6 Combining Like Terms Try This: Example 2 Combine like terms. Pre-Algebra 1-6 Combining Like Terms Try This: Example 2 Combine like terms. A. 2x + 5x – 4y + 3 2x + 5x – 4y + 3 Identify like terms. 7x – 4y + 3 Combine coefficients: 2 + 5 = 7 B. 9d + 7c – 4d – 2c 9d + 7c – 4d – 2c Identify like terms. 5d + 5c Combine coefficients: 9 – 4 = 5 and 7 – 2 = 5 C. 8g + c – 6 8g + c – 6 No like terms.

Pre-Algebra 1-6 Combining Like Terms To simplify an expression, perform all possible operations, including combining like terms.

Example 3: Simplifying Algebraic Expressions by Combining Like Terms Pre-Algebra 1-6 Combining Like Terms Example 3: Simplifying Algebraic Expressions by Combining Like Terms Simplify 6(5 + n) – 2n. 6(5 + n) – 2n 6(5) + 6(n) – 2n Distributive Property. 30 + 6n – 2n 6n and 2n are like terms. 30 + 4n Combine coefficients 6 – 2 = 4

Example 4: Solving Algebraic Expressions by Combining Like Terms Pre-Algebra 1-6 Combining Like Terms Example 4: Solving Algebraic Expressions by Combining Like Terms Solve x + 3x = 48. x + 3x = 48 Identify like terms. The coefficient of x is 1. 4x = 48 Combine coefficients: 1 + 3 = 4 4x = 48 Divide both sides by 4. 4 4 x = 12

Pre-Algebra 1-6 Combining Like Terms 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 power. Equivalent expressions have the same value for all values of the variables.

Pre-Algebra 1-6 Combining Like Terms To simplify an expression, perform all possible operations, including combining like terms.

1-6 Combining Like Terms Try This: Example 1 Combine like terms. Pre-Algebra 1-6 Combining Like Terms Try This: Example 1 Combine like terms. Identify like terms; the coefficient of q is 1, because 1q = q. A. 4q – q 3q Combine coefficients: 4 – 1 = 3 Identify like terms; the coefficient of c is 1, because 1c = c. B. 5c + 8 – 4c – 2 – c Combine coefficients: 5 – 4 – 1 = 0 and 8 – 2 = 6 6

1-6 Combining Like Terms Try This: Example 2 Combine like terms. Pre-Algebra 1-6 Combining Like Terms Try This: Example 2 Combine like terms. A. 2x + 5x – 4y + 3 2x + 5x – 4y + 3 Identify like terms. 7x – 4y + 3 Combine coefficients: 2 + 5 = 7 B. 9d + 7c – 4d – 2c 9d + 7c – 4d – 2c Identify like terms. 5d + 5c Combine coefficients: 9 – 4 = 5 and 7 – 2 = 5 C. 8g + c – 6 8g + c – 6 No like terms.

1-6 Combining Like Terms Try This: Example 3 Simplify 3(c + 7) – c. Pre-Algebra 1-6 Combining Like Terms Try This: Example 3 Simplify 3(c + 7) – c. 3(c + 7) – c 3(c) + 3(7) – c Distributive Property. 3c + 21 – c 3c and c are like terms. 2c + 21 Combine coefficients 3 – 1 = 2

1-6 Combining Like Terms Try This: Example 4 Solve 7c – c = 102. Pre-Algebra 1-6 Combining Like Terms Try This: Example 4 Solve 7c – c = 102. 7c – c = 102 Identify like terms. The coefficient of c is 1. 6c = 102 Combine coefficients: 7 – 1 = 6 6c = 102 Divide both sides by 6. 6 6 c = 17