78 Chapter 1 Real Numbers and Algebraic Expressions Like Terms Terms that have the same variables with the same exponents are like terms. Terms that do not have the same variables with the same exponents are unlike terms. Like Terms Unlike Terms 2x, -5x 2x, -5 y2, 4y2 y2, 4y -3xy, 7yx -3xy, 7x2y ���������������������� Identifying Like Terms Step: a. If the variables and exponents are the same, the terms are like. b. If the variables or exponents are different, the terms are unlike. �� ������������������������ ������������������ Determine if the terms are like or unlike and explain why. Problems Like Terms Unlike Terms Why? 2a. -9y and -9 X One term contains the variable y and the other term does not contain a variable. 2b. x and -8x X Each term contains the variable x. 2c. 2ba, 3ab, ab X Each term contains the variables ab. Recall ba = ab by the commutative property of multiplication. 2d. 6xy2 and 2x2y X These terms are unlike terms because the variables have different exponents. Student Check 2 Determine if the terms are like or unlike and explain why. a. 4h and 4 b. 2y and y c. 6rh and -6hr d. x2y and xy2 Combining Like Terms Algebraic expressions that contain like terms can be simplified by combining their like terms. There are two ways to think about combining like terms. Consider the algebraic expression 4x + 2x. The terms 4x and 2x are like terms. To simplify this expression, we can think of the problem in this way. 4x + 2x = x + x + x + x + x + x = 6x We can also use the distributive property to combine like terms. 4x + 2x = (4 + 2)x = 6x In either method, the result is the same, 4x + 2x = 6x. ���������������������� Combining Like Terms Step 1: Apply the distributive property to determine the coefficient of the like terms. Step 2: Simplify. Keep the variable component the same. �� ������������������������ ������������������ Simplify each expression by combining like terms, if possible. 3a. 2x + x 3b. 8x - x 3c. 4y2 + 3y2 3d. 3 + 5x 3e. x 2 + 5x 3f. -2a2 - 4a2 + 5a - 3a Objective 2 ▶ Identify like terms. Objective 3 ▶ Combine like terms.
hendricks_beginning_algebra_1e_ch1_3
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