Section 1.8 Algebraic Expressions 79 Solutions 3a. 2x + x = 2x + 1x Recall x = 1x. = (2 + 1)x Apply the distributive property. = 3x Simplify. It is not necessary to show the distributive property step. We can simply add the coefficients of the like terms mentally to get 2x + x = 2x + 1x = 3x 3b. 8x - x = 8x - 1x 8x - x = 8x - 1x = (8 - 1)x = 7x = 7x 3c. 4y2 + 3y2 = (4 + 3)y2 4y2 + 3y2 = 7y2 = 7y2 3d. The terms are unlike and therefore cannot be combined. 3e. x 2 + 5x = 1 2 x + 5x Recall that x 2 = 1x 2 = 1 2 x = a1 2 + 5b x Apply the distributive property. = a1 2 + 10 2 b x Write 5 as 10 2 = 11 2 x Add. 3f. There are two sets of like terms. Apply the distributive property for each set of like terms to get -2a2 - 4a2 + 5a - 3a = (-2 - 4)a2 + (5 - 3)a = -6a2 + 2a Adding the coefficients of the like terms and keeping the variables of the like terms the same gives us -2a2 - 4a2 + 5a - 3a = -6a2 + 2a Student Check 3 Simplify each expression by combining like terms, if possible. a. 11y + y b. 10b - b c. 2a2 + 9a2 d. 6 - 2x e. a 3 + 4a f. -3x2 - 4x2 + 7x - 6x Simplifying Algebraic Expressions Simplifying algebraic expressions is a skill that we use in most aspects of algebra. Simplifying algebraic expressions involves clearing parentheses and combining any like terms. ���������������������� Simplifying Algebraic Expressions Step 1: Clear any parentheses by applying the distributive property. Step 2: Combine like terms. Objective 4 ▶ Simplify algebraic expressions.
hendricks_beginning_algebra_1e_ch1_3
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