Sure! Let's simplify the expression given step-by-step. The expression to simplify is:
[tex]\[
2(a + b) + 3(a + b)
\][/tex]
### Step 1: Distribute the Constants Inside the Parentheses
First, we distribute the constants [tex]\(2\)[/tex] and [tex]\(3\)[/tex] inside the parentheses to both [tex]\(a\)[/tex] and [tex]\(b\)[/tex].
[tex]\[
2(a + b) = 2a + 2b
\][/tex]
[tex]\[
3(a + b) = 3a + 3b
\][/tex]
### Step 2: Combine the Distributed Terms
Now, we combine the results from the first step:
[tex]\[
2a + 2b + 3a + 3b
\][/tex]
### Step 3: Group and Combine Like Terms
Next, we group and combine the like terms (terms with [tex]\(a\)[/tex] and terms with [tex]\(b\)[/tex]):
[tex]\[
(2a + 3a) + (2b + 3b)
\][/tex]
[tex]\[
5a + 5b
\][/tex]
### Step 4: Write the Simplified Expression
The final simplified expression is:
[tex]\[
5a + 5b
\][/tex]
So, the simplified form of [tex]\(2(a + b) + 3(a + b)\)[/tex] is:
[tex]\[
5a + 5b
\][/tex]
