multiply x 2 )( 3x 4 using the foil method

Answer 1

To multiply the expressions \( (x + 2)(3x + 4) \) using the FOIL method, follow these steps:

FOIL stands for:

• First
• Outer
• Inner
• Last

1. First: Multiply the first terms in each binomial: \[ x \cdot 3x = 3x^2 \]

2. Outer: Multiply the outer terms in the expression: \[ x \cdot 4 = 4x \]

3. Inner: Multiply the inner terms: \[ 2 \cdot 3x = 6x \]

4. Last: Multiply the last terms in each binomial: \[ 2 \cdot 4 = 8 \]

Now, combine all these results: \[ 3x^2 + 4x + 6x + 8 \]

Combine the like terms (4x + 6x): \[ 3x^2 + 10x + 8 \]

So, the final result of multiplying \( (x + 2)(3x + 4) \) is: \[ \boxed{3x^2 + 10x + 8} \]