https://file.aiquickdraw.com/mathbot/file/17246801831229j7ykxy9.jpg

The equation given in the image is:

\[
\frac{1}{3}p^2 = \frac{12}{25}
\]

To factorize and solve this equation for \( p \), let's follow the steps below.

### Step-by-step Solution

1. **Clear the fractions by multiplying both sides by 3:**

   \[
   p^2 = 3 \times \frac{12}{25}
   \]

2. **Simplify the right-hand side:**

   \[
   p^2 = \frac{36}{25}
   \]

3. **Take the square root of both sides to solve for \( p \):**

   \[
   p = \pm \sqrt{\frac{36}{25}}
   \]

4. **Simplify the square root:**

   \[
   p = \pm \frac{\sqrt{36}}{\sqrt{25}}
   \]

   \[
   p = \pm \frac{6}{5}
   \]

### Conclusion

The solutions to the equation \(\frac{1}{3}p^2 = \frac{12}{25}\) are:

\[
p = \frac{6}{5} \quad \text{and} \quad p = -\frac{6}{5}
\]

Would you like more details on any specific step, or do you have any other questions?

Here are 5 related questions to explore further:

1. How do you solve equations involving fractions with variable terms?
2. What is the process of rationalizing a fraction, and when is it necessary?
3. How do you determine whether a quadratic equation will have real or complex solutions?
4. What are the differences between solving linear and quadratic equations?
5. Can all equations be solved by factoring, or are there limitations?

**Tip:** When solving quadratic equations, always consider both the positive and negative roots if you're taking the square root of both sides!

Learn how to factorize and solve the equation (1/3)p^2 = (12/25) with a detailed step-by-step solution. This problem covers key algebraic concepts, including equations, fractions, quadratic equations, and square roots. Suitable for Grades 9-12 students.

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