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A Question 4 (20 points) Retake question Identify the like terms, if any: \[ 7 a^{2} b, 2 a b, 8,-b a \] a) There are no like terms b) \( 2 a b \) c) 8 d) \( 7 a^{2} b \) e) \( -b a \)

Ask by Bush Willis. in the United States
Feb 26,2025

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Answer

The like terms are \( 2ab \) and \( -ba \).

Solution

To determine if terms are like terms, we look for terms that have exactly the same variable parts with the same exponents. The given terms are:   7a²b, 2ab, 8, –ba Examine each term: • 7a²b has the variable part a²b. • 2ab has the variable part ab. • 8 is a constant with no variable. • –ba is the same as –ab (multiplication is commutative) and has the variable part ab. Only the terms with the variable part ab are like terms. Here, 2ab and –ba (option b and option e) are like terms; they have identical variable parts. The term 7a²b is different because the exponent on a is 2, and the constant 8 has no variable. Thus, the like terms are:   2ab and –ba.

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Beyond the Answer

To identify like terms, we need to look for terms that have the same variables raised to the same powers. In this case: 1. \( 7 a^{2} b \): This term involves \( a \) squared and \( b \). 2. \( 2 a b \): This term has \( a \) to the first power and \( b \). 3. \( 8 \): This is a constant term (no variables at all). 4. \( -b a \): This term is equivalent to \( -a b \), which also has \( a \) to the first power and \( b \). The like terms are \( 2 a b \) and \( -b a \) since both have the same variables. Therefore, among the given options, the term that is part of this group is: b) \( 2 a b \)

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