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Problem 11

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

Expert verified
(a) The sum of the given algebraic expressions is $$8a$$. (b) The factored form of the given algebraic expression is $$c(5a + 2b)$$.
See the step by step solution

## 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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