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The expression provided is \((b - 5)^2\). To multiply or expand this expression, we use the formula for the square of a binomial:

\[
(a - b)^2 = a^2 - 2ab + b^2
\]

For \((b - 5)^2\):

1. \(a = b\)
2. \(b = 5\)

Now, applying the formula:

\[
(b - 5)^2 = b^2 - 2 \cdot b \cdot 5 + 5^2
\]

Calculating each term:

1. \(b^2\)
2. \(-2 \cdot b \cdot 5 = -10b\)
3. \(5^2 = 25\)

So, the expanded form is:

\[
(b - 5)^2 = b^2 - 10b + 25
\]

### Solution: 
\[
(b - 5)^2 = b^2 - 10b + 25
\]

Would you like further details on any part of this process?

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Here are related questions for further exploration:

1. How would you expand \((b + 5)^2\) using the same method?
2. What is the general formula for \((a - b)^n\) when \(n = 3\)?
3. Can this expansion process be applied to complex numbers?
4. How does the distributive property work in binomial expansions?
5. What is the difference between \((b - 5)^2\) and \((5 - b)^2\)?

**Tip:** Remember, squaring a binomial always involves three terms: the square of each term and twice the product of the two terms.

Learn how to expand the expression (b - 5)^2 using the formula for the square of a binomial. This guide provides a step-by-step solution and covers essential algebraic concepts, ideal for students in Grades 8-10.

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