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To expand and simplify the expression \((5h + 2)(h + 4)\), we use the distributive property (often referred to as FOIL in binomials):

\[
(5h + 2)(h + 4)
\]

First, distribute each term in the first binomial to every term in the second binomial:

\[
= (5h \cdot h) + (5h \cdot 4) + (2 \cdot h) + (2 \cdot 4)
\]

Now, calculate each multiplication:

\[
= 5h^2 + 20h + 2h + 8
\]

Next, combine the like terms:

\[
= 5h^2 + (20h + 2h) + 8
\]

\[
= 5h^2 + 22h + 8
\]

Thus, the expanded and simplified form of \((5h + 2)(h + 4)\) is:

\[
5h^2 + 22h + 8
\]

Let me know if you'd like further details!

Here are 5 related questions:
1. What is the general approach for expanding any two binomials?
2. How does the distributive property work with trinomials?
3. Can this method be extended to higher powers, like \((5h + 2)^2\)?
4. What does the FOIL method stand for and how is it used?
5. How would this expression change if a negative sign was involved, like \((5h - 2)(h + 4)\)?

**Tip:** When simplifying expressions, always group and combine like terms at the end to get the cleanest result.

Expand and simplify the expression (5h + 2)(h + 4) by applying the distributive property. Learn how to combine like terms to get the final simplified result of 5h^2 + 22h + 8. Ideal for students in Grades 8-10.

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