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Chapter 8: Chapter 8

Problem 138

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Add the expressions \(4 a^{2}-3+5 a, 6 a-2 a^{2}+2\), and \(2 a^{2}-3 a+8\)

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The sum of the expressions \(4a^2 - 3 + 5a\), \(6a - 2a^2 + 2\), and \(2a^2 - 3a + 8\) is \(4a^2 + 8a + 7\).
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TABLE OF CONTENTS :
TABLE OF CONTENTS

Step 1: Identify the like terms

In the given expressions, the like terms are those with the same variable raised to the same power. For our expressions, the like terms are: - \(4a^2, -2a^2\), and \(2a^2\) (all are terms with \(a^2\)) - \(5a\) and \(6a\), and \(-3a\) (all are terms with \(a\)) - \(-3, 2\), and \(8\) (all are constant terms)

Step 2: Add the coefficients of like terms

Now we will add the coefficients of the like terms together: - For the terms with \(a^2\): \(4a^2 - 2a^2 + 2a^2 = (4 - 2 + 2)a^2 = 4a^2\) - For the terms with \(a\): \(5a + 6a - 3a = (5 + 6 - 3)a = 8a\) - For the constant terms: \(-3 + 2 + 8 = -3 + 10 = 7\)

Step 3: Write the sum of the expressions

Combine the resulting terms to get the sum of the given expressions: \(4a^2 + 8a + 7\) So, the sum of the expressions \(4a^2 - 3 + 5a\), \(6a - 2a^2 + 2\), and \(2a^2 - 3a + 8\) is \(4a^2 + 8a + 7\).

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