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Simplifying Algebraic Expressions 7-1 Learn to combine like terms in an expression.

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Simplifying Algebraic Expressions 7-1 Vocabulary terms like terms equivalent expressions simplify

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Simplifying Algebraic Expressions 7-1 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

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Simplifying Algebraic Expressions 7-1 To simplify an expression, perform all possible operations, including combining like terms.

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Simplifying Algebraic Expressions 7-1 Combine like terms. Additional Example 1: Combining Like Terms To Simplify Identify like terms. Combine coefficients: 14 – 5 = 9 A. 14a – 5a 9a9a B. 7y 2 + 8 – 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

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Simplifying Algebraic Expressions 7-1 Combine like terms. Check It Out: Example 1 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

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Simplifying Algebraic Expressions 7-1 Combine like terms. Additional 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

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Simplifying Algebraic Expressions 7-1 Combine like terms. Additional Example 2B: Combining Like Terms in Two-Variable Expressions No like terms. 4m 3 + 9n – 2

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Simplifying Algebraic Expressions 7-1 Combine like terms. Check It Out: Example 2 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

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Simplifying Algebraic Expressions 7-1 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!

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Simplifying Algebraic Expressions 7-1 Simplify 6(5 + n) – 2n. Additional Example 3: Using the Distributive Property to Simplify Distributive Property. Multiply. 6(5 + n) – 2n 30 + 6n – 2n 6(5) + 6(n) – 2n 30 + 4n Combine coefficients: 6 – 2 = 4.

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Simplifying Algebraic Expressions 7-1 Simplify 3(c + 7) – c. Check It Out: Example 3 Distributive Property. Multiply. 3(c + 7) – c 3c + 21 – c 3(c) + 3(7) – c 2c + 21 Combine coefficients: 3 – 1 = 2.

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Simplifying Algebraic Expressions 7-1 Solve x + 3x = 48. Additional Example 4: Combining Like Terms to Solve Algebraic Equations Identify like terms. The coefficient of x is 1. Combine coefficients: 1 + 3 = 4 x + 3x = 48 4x = 48 x = 12 Divide both sides by 4. 4 4

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Simplifying Algebraic Expressions 7-1 Solve 7c – c = 102. Check It Out: Example 4 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 6. 6 6

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Simplifying Algebraic Expressions 7-1 Lesson Quiz Combine like terms. 1. 3x 2 + 4 + 2x 2 2. 13k + 6 – 8m + 9 + k Simplify. 3. 4(3x + 6) – 7x 4. 6(x + 5) + 3x Solve. 5. 6y + y = 42 6. The Accounting Department ordered 15 boxes of pens. The Marketing Department ordered 9 boxes of pens. If the total cost of the combined order was $72, what is the price of each box of pens? 14k – 8m + 15 y = 6 5x 2 + 4 5x + 249x + 30 $3

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