The given expression is:

\[
25y^2 - 30y + 9
\]

This is a quadratic expression in terms of \( y \). To simplify or factorize it, let's check if it's factorable.

### Factoring the expression:

1. Check if it's a perfect square trinomial:
   - The first term \( 25y^2 \) is a perfect square because \( (5y)^2 = 25y^2 \).
   - The last term \( 9 \) is a perfect square because \( 3^2 = 9 \).
   - Check the middle term: \( 2 \times 5y \times 3 = 30y \), which matches the middle term of \( -30y \), but with a negative sign.

Therefore, we can factor this as:

\[
25y^2 - 30y + 9 = (5y - 3)^2
\]

So, the factored form is:

\[
(5y - 3)^2
\]

Would you like more details on how I arrived at this, or do you have any questions?

Here are five related questions to consider:

1. How do you solve quadratic equations using the factorization method?
2. What is a perfect square trinomial, and how is it identified?
3. How would the factorization change if the middle term was positive, i.e., \( +30y \)?
4. Can the quadratic formula be used to solve this expression? If so, how?
5. What are the roots of the equation \( 25y^2 - 30y + 9 = 0 \)?

**Tip:** Always check if the quadratic expression is a perfect square before trying other methods like completing the square or using the quadratic formula.

Learn how to factor the quadratic expression 25y^2 - 30y + 9 into a perfect square trinomial with this step-by-step guide. This problem explores key algebraic concepts like factoring and perfect square trinomials. Ideal for students in Grades 8-10.

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