To simplify $(p - 3q)^2 + 4pq$, we can expand the square term and then combine like terms. Let's go through it step-by-step:

Step 1: Expand $(p - 3q)^2$

Using the formula $(a - b)^2 = a^2 - 2ab + b^2$, we get: $(p - 3q)^2 = p^2 - 2 \cdot p \cdot 3q + (3q)^2$ $= p^2 - 6pq + 9q^2$

Step 2: Rewrite the Expression

Now, substitute this expansion back into the original expression: $(p - 3q)^2 + 4pq = p^2 - 6pq + 9q^2 + 4pq$

Step 3: Combine Like Terms

Now, combine the $pq$ terms: $= p^2 - 6pq + 4pq + 9q^2$ $= p^2 - 2pq + 9q^2$

Final Answer

The simplified expression is: $p^2 - 2pq + 9q^2$

Would you like further clarification on any step?

Here are five related questions for further practice:

1. How would you simplify $(p + 3q)^2 - 4pq$?
2. What is the expanded form of $(p + q)^3$?
3. How do you simplify $(2p - 4q)^2 + 8pq$?
4. How would you factor the expression $p^2 - 2pq + q^2$?
5. What is the result of expanding $(a - b)(a + b)$?

Tip: When simplifying expressions with squares, always look for opportunities to combine like terms after expanding.