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Problem 10

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\((3 x+1)^{2}\)

Short Answer

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The expanded form of the given expression \((3x+1)^2\) is \(9x^2 + 6x + 1\).

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Step by step solution

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TABLE OF CONTENTS

Step 1: Identify the values of a and b

In the expression \((3x + 1)^2\), we can see that \(a = 3x\) and \(b = 1\).

Step 2: Apply the binomial square formula

Use the formula \((a+b)^2 = a^2 + 2ab + b^2\), and substitute the values of \(a\) and \(b\) that we identified in Step 1. \((3x+1)^2 = (3x)^2 + 2(3x)(1) + (1)^2\)

Step 3: Simplify the terms

Simplify each term in the expanded expression: \((3x)^2 = 9x^2\) \(2(3x)(1) = 6x\) \((1)^2 = 1\)

Step 4: Combine the simplified terms

Combine the simplified terms from Step 3 to obtain the final expanded expression: \((3x+1)^2 = 9x^2 + 6x + 1\) So, the expanded form of the given expression is \(9x^2 + 6x + 1\).

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Chapter 0: Chapter 0

\((3 x+1)^{2}\)

Short Answer

Step by step solution

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Step 1: Identify the values of a and b

Step 2: Apply the binomial square formula

Step 3: Simplify the terms

Step 4: Combine the simplified terms

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More chapters from the book ‘Finite Mathematics and Applied Calculus’

Chapter 1

Chapter 2

Chapter 3

Chapter 4

Chapter 5

Chapter 6

Chapter 7

Chapter 8

Chapter 9

Chapter 10

Chapter 11

Chapter 12

Chapter 13

Chapter 14

Chapter 15

Chapter 16

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