To expand the expression \((a-1)(a+4)\), we use the distributive property (also known as the FOIL method for binomials):

\[
(a-1)(a+4)
\]

This means we multiply each term in the first binomial by each term in the second binomial:

1. \(a \cdot a = a^2\)
2. \(a \cdot 4 = 4a\)
3. \(-1 \cdot a = -a\)
4. \(-1 \cdot 4 = -4\)

Now, combine all these products:

\[
a^2 + 4a - a - 4
\]

Combine like terms:

\[
a^2 + 3a - 4
\]

So, the expanded form of \((a-1)(a+4)\) is:

\[
\boxed{a^2 + 3a - 4}
\]

Would you like more details on this process or have any other questions?

Here are 5 numbered questions you might be interested in:
1. How do you factorize quadratic equations?
2. Can you explain the distributive property in more detail?
3. How do you solve quadratic equations?
4. What are the different methods for expanding binomials?
5. Can you provide examples of using the FOIL method in other expressions?

Tip: Always remember to combine like terms when simplifying expressions to ensure accuracy.

Discover how to expand the expression (a-1)(a+4) using the FOIL method with a clear, step-by-step explanation. This topic covers essential algebraic concepts, including binomial expansion and combining like terms, perfect for students in Grades 7-9.

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