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The exercise asks to factorize perfect square trinomials. Let's solve each one step by step:

### 1. \( x^2 + 6x + 9 \)
This is a perfect square because:
\[
x^2 + 6x + 9 = (x + 3)^2
\]

### 2. \( a^2 + 72a + 1296 \)
Factoring:
\[
a^2 + 72a + 1296 = (a + 36)^2
\]

### 3. \( b^2 - 16b + 64 \)
Factoring:
\[
b^2 - 16b + 64 = (b - 8)^2
\]

### 4. \( 9x^2 + 12x + 4 \)
Factoring:
\[
9x^2 + 12x + 4 = (3x + 2)^2
\]

### 5. \( 64y^2 - 64y + 16 \)
Factoring:
\[
64y^2 - 64y + 16 = (8y - 4)^2
\]

### 6. \( 36m^2 + 96m + 64 \)
Factoring:
\[
36m^2 + 96m + 64 = (6m + 8)^2
\]

### 7. \( 49n^2 + \frac{14n}{3} + \frac{1}{9} \)
Factoring:
\[
49n^2 + \frac{14n}{3} + \frac{1}{9} = \left(7n + \frac{1}{3}\right)^2
\]

### 8. \( \frac{25}{4}g^2 - 5g + \frac{1}{4} \)
Factoring:
\[
\frac{25}{4}g^2 - 5g + \frac{1}{4} = \left(\frac{5g}{2} - \frac{1}{2}\right)^2
\]

### 9. \( x^2 - 10x + 25 \)
Factoring:
\[
x^2 - 10x + 25 = (x - 5)^2
\]

### 10. \( 2x^2 + 20x + 50 \)
Factoring:
\[
2x^2 + 20x + 50 = 2(x^2 + 10x + 25) = 2(x + 5)^2
\]

Would you like further details on any specific problem, or have any questions?

### Related Questions:
1. How do you identify a perfect square trinomial?
2. What is the general form of a perfect square trinomial?
3. How can factoring help solve quadratic equations?
4. What are some common mistakes when factoring perfect square trinomials?
5. How do you factor trinomials that are not perfect squares?

**Tip:** Always check if a trinomial is a perfect square by comparing it with \((a + b)^2\).

Factor the perfect square trinomials from the given set of expressions.

Learn how to factor perfect square trinomials with detailed, step-by-step solutions. This exercise covers key algebraic concepts, including factoring quadratic equations. Suitable for students in Grades 8-10.

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