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Let's go through the factoring problems one by one.

### 1. \( 9x^2 + 24x + 16 \)
This is a quadratic trinomial. We can factor it by finding two numbers that multiply to \( 9 \times 16 = 144 \) and add to \( 24 \).

The factors of 144 that add up to 24 are 12 and 12. Therefore:

\[
9x^2 + 24x + 16 = (3x + 4)(3x + 4) = (3x + 4)^2
\]

### 2. \( 25x^2 - 40xy + 16y^2 \)
This is a perfect square trinomial. We can factor it by recognizing it as the square of a binomial:

\[
25x^2 - 40xy + 16y^2 = (5x - 4y)^2
\]

### 3. \( 4x^2 + 12x + 9 \)
This is another quadratic trinomial. Again, we'll factor it by finding two numbers that multiply to \( 4 \times 9 = 36 \) and add to \( 12 \).

The factors of 36 that add up to 12 are 6 and 6. Therefore:

\[
4x^2 + 12x + 9 = (2x + 3)(2x + 3) = (2x + 3)^2
\]

These are the factorizations of the given expressions.

Would you like more details on any of these steps, or do you have any questions?

### Related Questions:
1. How can you identify a perfect square trinomial?
2. What is the general form of a quadratic trinomial?
3. How do you factor trinomials when they are not perfect squares?
4. Can every quadratic trinomial be factored? If not, what other methods can you use to solve them?
5. How do you factor the difference of squares?

### Tip:
When factoring, always check for a greatest common factor (GCF) first before proceeding with other methods.

Factor the given expressions:
1. 9x^2 + 24x + 16
2. 25x^2 - 40xy + 16y^2
3. 4x^2 + 12x + 9

Learn how to factor quadratic expressions such as 9x^2 + 24x + 16, 25x^2 - 40xy + 16y^2, and 4x^2 + 12x + 9. This tutorial covers algebraic concepts related to factoring perfect square trinomials, suitable for students in Grades 8-10.

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