Question

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:**
- **F**irst
- **O**uter
- **I**nner
- **L**ast

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:
\[
\boxed{3x^2 + 10x + 8}
\]