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Let's factor these expressions step by step.

### 1. **Factorise fully: \( 15x^3 + 3x^2y \)**

We start by finding the greatest common factor (GCF) of the terms \( 15x^3 \) and \( 3x^2y \).

- The GCF of \( 15 \) and \( 3 \) is \( 3 \).
- The GCF of \( x^3 \) and \( x^2 \) is \( x^2 \).

Thus, the common factor is \( 3x^2 \).

Now factor out \( 3x^2 \) from both terms:

\[
15x^3 + 3x^2y = 3x^2(5x + y)
\]

So, the fully factorised form is:

\[
3x^2(5x + y)
\]

---

### 2. **Factorise fully: \( 4p^2 - 36 \)**

This is a difference of squares. We can rewrite it as:

\[
4p^2 - 36 = 4(p^2 - 9)
\]

Now, \( p^2 - 9 \) is also a difference of squares:

\[
p^2 - 9 = (p - 3)(p + 3)
\]

Thus, the fully factorised form is:

\[
4(p - 3)(p + 3)
\]

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Let me know if you'd like more details or explanations!

Here are five related questions to deepen your understanding:
1. How would you factorise the expression \( 9x^3 + 6x^2y \)?
2. What is the factored form of \( 16p^2 - 25 \)?
3. How would you identify and factor common factors from the expression \( 12x^4 - 8x^3y \)?
4. How can you factor \( 25x^2 - 1 \) using the difference of squares?
5. What is the process for factorising \( 8x^2 + 12xy \)?

**Tip:** Always check for the greatest common factor (GCF) first before proceeding with other factorisation techniques!

Factorise fully 15x^3 + 3x^2y and 4p^2 - 36.

Learn how to fully factorise the algebraic expressions 15x^3 + 3x^2y by finding the greatest common factor and 4p^2 - 36 using the difference of squares method. This step-by-step guide is suitable for students in Grades 8-10.

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