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Chapter 1: Chapter 1

Problem 11

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(a) Add, \(3 \mathrm{a}+5 \mathrm{a}\) (b) Factor, \(5 \mathrm{ac}+2 \mathrm{bc}\).

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(a) The sum of the given algebraic expressions is \(8a\). (b) The factored form of the given algebraic expression is \(c(5a + 2b)\).
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TABLE OF CONTENTS :
TABLE OF CONTENTS

Step 1: (a) Add the algebraic expressions

To add algebraic expressions with the same variable, we simply add their coefficients. Here, we have: \(3a + 5a\)

Step 2: Calculate the sum

Add the coefficients of 'a' to get the sum: \(3a + 5a = (3 + 5)a\) \(= 8a\) So, the sum of the given algebraic expressions is 8a.

Step 3: (b) Identify the common factor

To factor an algebraic expression, we first identify the greatest common factor (GCF) shared by all the terms. In this case, we have: \(5ac + 2bc\) The GCF here is 'c', because both terms have 'c' in common.

Step 4: Factor out the GCF

Next, we factor out the GCF from each of the terms: \(c(5a + 2b)\) So, the factored form of the given algebraic expression is \(c(5a + 2b)\).

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