The function you've provided is:

\[
h(x) = (8 - x)(x + 3)
\]

To simplify this, we can expand the expression using the distributive property (also known as the FOIL method for binomials).

\[
h(x) = (8 - x)(x + 3)
\]

Expanding:

\[
h(x) = 8(x + 3) - x(x + 3)
\]

Now, distribute each term:

\[
h(x) = 8x + 24 - x^2 - 3x
\]

Combine like terms:

\[
h(x) = -x^2 + 8x - 3x + 24
\]
\[
h(x) = -x^2 + 5x + 24
\]

Thus, the simplified form of the function is:

\[
h(x) = -x^2 + 5x + 24
\]

Would you like further details on this or have any questions?

Here are 5 related questions to expand your understanding:
1. How would you find the vertex of the quadratic function \( h(x) = -x^2 + 5x + 24 \)?
2. What is the domain and range of \( h(x) \)?
3. How would you determine the x-intercepts of \( h(x) \)?
4. What is the maximum value of \( h(x) \), and at what value of \( x \) does it occur?
5. How does the negative coefficient of \( x^2 \) affect the shape of the graph?

**Tip:** A quadratic function like \( -x^2 + bx + c \) has a parabolic graph that opens downward when the coefficient of \( x^2 \) is negative.

Explore how to simplify the quadratic expression h(x) = (8 - x)(x + 3) step-by-step. This solution demonstrates the use of binomial expansion, distributive property, and results in a standard quadratic form. Suitable for students in Grades 9-11.

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