To expand and simplify the given expression [tex]\( 2(4x + 2) + 3(x + 2) \)[/tex], we need to follow a step-by-step approach.
### Step 1: Distribute the constants inside the parentheses
First, let's distribute the constants outside each set of parentheses to the terms inside the parentheses:
For [tex]\(2(4x + 2)\)[/tex]:
[tex]\[ 2 \cdot 4x + 2 \cdot 2 = 8x + 4 \][/tex]
For [tex]\( 3(x + 2) \)[/tex]:
[tex]\[ 3 \cdot x + 3 \cdot 2 = 3x + 6 \][/tex]
### Step 2: Combine the expanded terms
After distributing, we obtain:
[tex]\[ 8x + 4 + 3x + 6 \][/tex]
### Step 3: Combine like terms
Next, we combine the terms that contain [tex]\(x\)[/tex] and the constant terms separately.
Combining the [tex]\(x\)[/tex] terms:
[tex]\[ 8x + 3x = 11x \][/tex]
Combining the constant terms:
[tex]\[ 4 + 6 = 10 \][/tex]
### Final Answer:
So, the expanded and simplified form of the expression [tex]\(2(4x + 2) + 3(x + 2)\)[/tex] is:
[tex]\[ 11x + 10 \][/tex]
