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Algebra 1 Lesson Notes 2.5A Date ________________ Objective: Apply the distributive property. equivalent expressions: two expressions that have the same value for all values of the variable. Distributive Property: For real numbers a, b, and c, a(b + c) = ab + ac (b + c)a= ba + ca a(b – c) = ab – ac (b – c)a = ba – ca A factor outside the parentheses must multiply each term in the parentheses. Example 1 (p 96): Apply the distributive property Use the distributive property to write an equivalent expression. a. 3(x + 6) b. (n + 5)n c. y(x + y – 12) d. (8 – x)9 Example 2 (p 97): Distribute a negative number a. (y – 2)(– 4) b. − 5x(4 − x) c. − (3y − 9) d. (3c – 8)(– 5) 478163423 Page 1 of 5 Challenge Example: Distributive property in reverse! This is called factoring. a. − 20a + 5b = ____(− 4a + b) b. 4c – 10d = ____( ___c – ___d) c. − 36x2 – 24x = ______(9x + 6) d. 18xy2 – 8x2y = _______( 9____ − 4x____) HW 478163423 A4 pp 99-101 #2-20 even, 56-67 Page 2 of 5 Algebra 1 Lesson Notes 2.5B Date ________________ Objective: Combine like terms. terms: the parts of an expression that are combined (added and subtracted) coefficient: the number part of a term with a variable constant or constant term: a term with a number but no variable part like terms: terms that have exactly the same variable parts; constant terms are like terms because they all have no variable 3 terms x 3x 12 coefficients are –1 and 3 12 is a constant − x and 3x are like terms Example 3 (p 97): Identify parts of an expression Identify the terms, like terms, coefficients, and constant terms of the expression: 478163423 a. 2 x 8 6 x 5 b. 2 y 8 6y 1 Page 3 of 5 Combining like terms: the process of combining terms that have the same variable parts. The distributive property (in reverse) lets you combine like terms that have variables. (Addition and subtraction let you combine the constants!) 2 x 8 6 x 5 like terms are −2x and 6x, so −2x + 6x = (−2 + 6)x = 4x −8 and 5 are also like terms, so −8 + 5 = −3 To combine like terms, combine (add or subtract) the coefficients of the like terms but DO NOT CHANGE the variable parts!!!! Simplified expression: an expression is simplified if it has no grouping symbols and all of the like terms have been combined. From above: 2 x 8 6 x 5 = 4x − 3 simplified expression NOTE: To simplify an expression, FIRST use the distributive property to eliminate any grouping symbols, THEN combine like terms. Example 4 (p 98): Simplifying an expression Which expression is equivalent to 6(x + 3) – 2(8 + x)? a. 4x + 2 478163423 b. 4x + 34 c. 8x + 2 d. 8x + 34 Page 4 of 5 Example 5 (p 98): Solve a multi-step problem Ms. Jenkins rented a rototiller from a garden shop. The rental charge is $28 per day for the first two days and then $15 per day for each additional day. a. Write an equation for t, the total charge, as a function of d, the number of days she rents the rototiller. b. If Ms. Jenkins kept the rototiller for 13 days, what was the total rental charge? HW 478163423 A5 pp 99-101 #21-27, 29-41 odd, 47-48, 50-52 Page 5 of 5