$$ \text{what is (fg)(x) if }f\left(x\right)=x_{}^2-16\text{ ; and }g\left(x\right)=5x+15\text{?} $$

The function $(fg)(x)$ is the product of $f(x)$ and $g(x)$, which means you multiply the two given functions $f(x)$ and $g(x)$.

Given:
\[
f(x) = x^2 - 16
\]
\[
g(x) = 5x + 15
\]

To find $(fg)(x)$, multiply $f(x)$ by $g(x)$:
\[
(fg)(x) = (x^2 - 16)(5x + 15)
\]

Now expand the product:
\[
(fg)(x) = x^2(5x + 15) - 16(5x + 15)
\]

Distribute the terms:
\[
(fg)(x) = x^2(5x) + x^2(15) - 16(5x) - 16(15)
\]
\[
(fg)(x) = 5x^3 + 15x^2 - 80x - 240
\]

Thus, the result is:
\[
(fg)(x) = 5x^3 + 15x^2 - 80x - 240
\]

Would you like more details on the steps or have any questions?

Here are 5 related questions for practice:
1. What is $(f+g)(x)$ for the same $f(x)$ and $g(x)$?
2. How do you find $(f/g)(x)$ if $g(x) \neq 0$?
3. Can you determine $(f \circ g)(x)$ (composition of functions)?
4. What is the derivative of $f(x)$?
5. What is the factored form of $f(x)$?

**Tip:** When multiplying polynomials, distributing each term carefully helps avoid errors in expansion.

what is (fg)(x) if f(x)=x^2-16 and g(x)=5x+15?

Learn how to multiply the polynomials f(x)=x^2-16 and g(x)=5x+15 to find (fg)(x). This detailed solution walks you through the expansion using the distributive property and provides a step-by-step explanation of the process. Suitable for Grades 9-10 students studying Algebra.

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