Question

using the foil method to find the product below. (x+5)(x^2-3x)

Answer 1

To find the product of \( (x + 5)(x^2 - 3x) \) using the FOIL method, we first clarify that the FOIL method is typically used for multiplying two binomials. However, since one of the factors here is a trinomial, we will systematically distribute each term in \( (x + 5) \) to every term in \( (x^2 - 3x) \).

Here's how it works:

1. **Distribute \( x \)**:
- \( x \cdot x^2 = x^3 \)
- \( x \cdot (-3x) = -3x^2 \)

2. **Distribute \( 5 \)**:
- \( 5 \cdot x^2 = 5x^2 \)
- \( 5 \cdot (-3x) = -15x \)

Now, we can combine all these products together:

\[
x^3 - 3x^2 + 5x^2 - 15x
\]

Next, we combine like terms:

\[
x^3 + ( -3x^2 + 5x^2) - 15x = x^3 + 2x^2 - 15x
\]

Thus, the final result of multiplying \( (x + 5)(x^2 - 3x) \) is:

\[
\boxed{x^3 + 2x^2 - 15x}
\]