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:
-
Distribute \( x \):
- \( x \cdot x^2 = x^3 \)
- \( x \cdot (-3x) = -3x^2 \)
-
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:
\[ \boxed{x^3 + 2x^2 - 15x} \]