The expression \((-y + 5)^2\) can be expanded using the formula for the square of a binomial:

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

Here, \( a = 5 \) and \( b = y \), so:

\[
(-y + 5)^2 = 5^2 - 2(5)(y) + y^2
\]

Now, calculate each term:

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

Thus, the expanded form is:

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

Would you like more details or have any questions?

Here are 5 related questions:
1. How would you expand \((2x - 3)^2\)?
2. What is the difference between \((y + 5)^2\) and \((-y + 5)^2\)?
3. How do you factor the expression \(y^2 - 10y + 25\)?
4. What is the geometric interpretation of \((-y + 5)^2\)?
5. How would you solve the equation \((-y + 5)^2 = 0\)?

**Tip:** When expanding binomials, always apply the square of a binomial formula carefully to avoid sign errors.

Learn how to expand the binomial (-y + 5)^2 using the square of a binomial formula. This problem covers key algebraic concepts and is suitable for students in Grades 8-10. The step-by-step solution includes identifying key terms and performing the binomial expansion.

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