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Chapter 15: Chapter 15

Problem 358

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Find A) \(4 a^{2} b+2 a b\) B) \(9 a b^{2} c-6 a^{2} c+12 a c\) C) \(\mathrm{ac}+\mathrm{bc}+\mathrm{ad}+\mathrm{bd}\)

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The simplified expressions are: A) \(2ab(2a+1)\) B) \(3ac(3b^2-2a+4)\) C) \((a+b)(c+d)\)
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TABLE OF CONTENTS :
TABLE OF CONTENTS

Step 1: Identify common factors

In this expression, we can see that both terms have \(a\) and \(b\) as their common factors.

Step 2: Factor out the common factors

We can factor out \(ab\) from both terms: \[ab(4a+2)\]

Step 3: Simplify the expression

Now, we can simplify the expression further by factoring out the common factor \(2\) from the parentheses: \[2ab(2a+1)\] So, the simplified expression for A is: \[2ab(2a+1)\] B) \(9ab^2c-6a^2c+12ac\)

Step 1: Identify common factors

In this expression, we can see that all three terms have \(a\) and \(c\) as their common factors.

Step 2: Factor out the common factors

We can factor out \(ac\) from all three terms: \[ac(9b^2-6a+12)\]

Step 3: Simplify the expression

Now, we can simplify the expression further by factoring out the common factor \(3\) from the parentheses: \[3ac(3b^2-2a+4)\] So, the simplified expression for B is: \[3ac(3b^2-2a+4)\] C) \(ac+bc+ad+bd\)

Step 1: Identify terms with common factors

In this expression, we can see that the first and third terms have \(a\) as a common factor, and the second and fourth terms have \(b\) as a common factor.

Step 2: Factor out the common factors

We can factor out \(a\) from the first and third terms and \(b\) from the second and fourth terms: \[a(c+d)+b(c+d)\]

Step 3: Simplify the expression

Now, we can simplify the expression further by factoring out the common factor \((c+d)\): \[(a+b)(c+d)\] So, the simplified expression for C is: \[(a+b)(c+d)\]

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