Question

multiply x 2 )( 3x 4 using the foil method. is it a (x-2)(3x)+(3x)(4)
(x)(3x)+4(x)+3x+4
(x)(3x+4)+(x-2)
((x-2)(3x)+(x-2)(4)

Answer 1

To multiply \( (x - 2)(3x + 4) \) using the FOIL method, we use the following steps:

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

2. **Outer**: Multiply the outer terms of the binomials:
\[
x \cdot 4 = 4x
\]

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

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

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

Combining like terms gives:
\[
3x^2 - 2x - 8
\]

So the final result of multiplying \( (x - 2)(3x + 4) \) using the FOIL method is:
\[
3x^2 - 2x - 8
\]

Based on your provided choices, the correct option corresponding to FOIL multiplication is \((x-2)(3x)+(x-2)(4)\), as this illustrates the concept of distributing each term in the first binomial to each term in the second binomial.