Question

Use the FOIL method to find the product below.
(x - 6)(x2+4x)
0x3-2x2-24x
0x3-10x2-24
043-2x2-24
0x3-10x2-24x

Answer 1

To use the FOIL method on the expression \((x - 6)(x^2 + 4x)\), we need to distribute each term in the first parentheses by each term in the second parentheses.

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

2. **Outer**: Multiply the outer terms in each binomial:
\[
x \cdot 4x = 4x^2
\]

3. **Inner**: Multiply the inner terms in each binomial:
\[
-6 \cdot x^2 = -6x^2
\]

4. **Last**: Multiply the last terms in each binomial:
\[
-6 \cdot 4x = -24x
\]

Now, we combine all these results:
\[
x^3 + 4x^2 - 6x^2 - 24x
\]

Next, we combine like terms:
\[
x^3 + (4x^2 - 6x^2) - 24x = x^3 - 2x^2 - 24x
\]

Thus, the final product is:
\[
x^3 - 2x^2 - 24x
\]

So the equivalent choice from the provided options is:
\[
0x^3 - 2x^2 - 24x \quad \text{(which can be simplified to } x^3 - 2x^2 - 24x \text{ since "0" does not affect the result)}
\]

This means the product of \((x - 6)(x^2 + 4x)\) is:
\[
x^3 - 2x^2 - 24x
\]