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Expand and simplify: [tex]2(4x + 2) + 3(x + 2)[/tex]

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Answer:

Sagot :

GinnyAnsweridn
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]
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