Question

which line shows the correct and complete distribution for the problem below
(2x + 3) (3x - 1)

Answer 1

To distribute the expression \((2x + 3)(3x - 1)\), you'll use the distributive property (often called the FOIL method for binomials, which stands for First, Outside, Inside, Last).

Here’s how to distribute:

1. **First**: Multiply the first terms in each binomial:
\[
2x \cdot 3x = 6x^2
\]

2. **Outside**: Multiply the outer terms:
\[
2x \cdot (-1) = -2x
\]

3. **Inside**: Multiply the inner terms:
\[
3 \cdot 3x = 9x
\]

4. **Last**: Multiply the last terms in each binomial:
\[
3 \cdot (-1) = -3
\]

Now, combine all these results:
\[
6x^2 - 2x + 9x - 3
\]

Combine like terms (\(-2x + 9x\)):
\[
6x^2 + 7x - 3
\]

So, the final result of the distribution of \((2x + 3)(3x - 1)\) is:
\[
6x^2 + 7x - 3
\]