https://file.aiquickdraw.com/mathbot/file/17273680951308oen91jt.jpg

The expression you have uploaded is:

\[
(y + 5) \cdot (5 - y)
\]

To simplify this expression, we can apply the distributive property (also known as FOIL for binomials):

\[
(y + 5)(5 - y) = y \cdot 5 + y \cdot (-y) + 5 \cdot 5 + 5 \cdot (-y)
\]

Now simplify each term:

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

Now, combining all these terms together:

\[
5y - y^2 + 25 - 5y
\]

The \(5y\) and \(-5y\) cancel out, leaving us with:

\[
-y^2 + 25
\]

Thus, the simplified expression is:

\[
25 - y^2
\]

Would you like further details or have any questions?

Here are five related questions to consider:
1. How would you solve the equation if it was set equal to zero: \((y + 5)(5 - y) = 0\)?
2. Can you rewrite this result, \(25 - y^2\), as a difference of squares?
3. What are the critical points or roots of the equation \(25 - y^2 = 0\)?
4. How would this expression change if we had a different binomial, such as \((y + 5)(y - 5)\)?
5. Can you explain the geometric interpretation of this expression as a parabola?

**Tip**: Whenever you simplify binomial products, the distributive property (FOIL) helps organize terms efficiently.

Simplify the expression (y + 5)(5 - y) using the distributive property. This solution demonstrates key algebraic concepts such as binomial expansion and the difference of squares. Suitable for students in Grades 8-10.

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