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Chapter 1: Problem 11

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

Short Answer

Expert verified
(a) The sum of the given algebraic expressions is \(8a\). (b) The factored form of the given algebraic expression is \(c(5a + 2b)\).

Step by step solution

01

(a) Add the algebraic expressions

To add algebraic expressions with the same variable, we simply add their coefficients. Here, we have: \(3a + 5a\)
02

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.
03

(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.
04

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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Most popular questions from this chapter

Evaluate \(p=\\{(a-b)(a b+c)\\} /(c b-2 a)\) When \(a=+2, b=-1 / 2\), and \(c=-3\)

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Simplify the following expressions, removing the parentheses 1) \(a+(b-c)\) 2) \(a x-(b y-c)\) 3) \(2-(-x+y)\)

Find the sum \(8+(-3)\).

Show that \((-2)+(-3)=-5\).
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