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Chapter 2: Problem 1

A. How many terms are in the expression \(5 t+3 s+2 t ?\) B. What are the coefficients? C. What are the like terms? D. Simplify the expression by combining like terms.

Short Answer

Expert verified
Question: Identify the number of terms, coefficients, and like terms in the expression \(5t + 3s + 2t\), and then simplify the expression by combining the like terms. Answer: In the expression \(5t + 3s + 2t\), there are 3 terms and the like terms are \(5t\) and \(2t\). The coefficients in the terms are 5, 3, and 2. To simplify the expression, we combine the like terms to get \(7t + 3s\).

Step by step solution

01

A. Identifying the number of terms

To find the number of terms in the given expression \(5t + 3s + 2t\), look for separate terms connected by addition or subtraction signs. In this expression, we have 3 terms: \(5t\), \(3s\), and \(2t\).
02

B. Identifying the coefficients

The coefficients are the numbers multiplying the variables in each term. In this case, the coefficients are: - In the term \(5t\), the coefficient is 5. - In the term \(3s\), the coefficient is 3. - In the term \(2t\), the coefficient is 2.
03

C. Identifying like terms

Like terms are terms that have the same variables raised to the same power. In this expression, the like terms are \(5t\) and \(2t\) since both have the same variable, \(t\), raised to the same power, which is 1.
04

D. Simplifying the expression by combining like terms

To simplify the expression, combine the like terms. In this case, we can combine the terms \(5t\) and \(2t\). When combining like terms, we add or subtract their coefficients and keep their variables raised to the same power. So, \(5t + 2t = (5+2)t = 7t\) Now substitute this back into the original expression: \(7t + 3s\) The simplified expression is \(7t + 3s\).

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