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The problem you've provided involves the binomial expansion of \((a - b)^5\). Using the binomial theorem, the expansion of \((a - b)^5\) can be written as:

\[
(a - b)^5 = \sum_{k=0}^{5} \binom{5}{k} a^{5-k}(-b)^k
\]

This formula expands as:

\[
a^5 - 5a^4b + 10a^3b^2 - 10a^2b^3 + 5ab^4 - b^5
\]

Now, let’s identify the specific terms mentioned in your problem:

1. **Term with \(a^2\)**:
   The term containing \(a^2b^3\) is the fourth term in the expansion, which is:
   \[
   -10a^2b^3
   \]
   Therefore, the coefficient is \(-10\).

2. **Term with \(b^4\)**:
   The term containing \(ab^4\) is the fifth term in the expansion, which is:
   \[
   5ab^4
   \]
   Therefore, the coefficient is \(5\).

Thus:
- The term in \(a^2\) is \(-10a^2b^3\),
- The term in \(b^4\) is \(5ab^4\).

Would you like further clarification or a breakdown of any part of this? Here are some follow-up questions you might find useful:

1. How does the binomial theorem work for different powers?
2. What is the general formula for a binomial expansion?
3. How do you determine the coefficients in a binomial expansion?
4. Can you explain the meaning of the binomial coefficient \(\binom{n}{k}\)?
5. How does the sign change affect the terms in the expansion?

**Tip:** Always remember that in binomial expansions, the signs alternate depending on whether the binomial has a negative or positive term inside!

In the expansion of (a - b)^5, find the term in a^2 and the term in b^4.

Learn how to find the specific terms in the binomial expansion of (a - b)^5. This problem focuses on identifying the terms with a^2 and b^4 using the binomial theorem. Suitable for Grades 9-11.

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