Let's break down $(2a - 3b)^2$ step by step.

What does $(2a - 3b)^2$ mean?

When you square something, you multiply it by itself. So, $(2a - 3b)^2$ means:

$(2a - 3b) \times (2a - 3b)$

Use the distributive property (FOIL method):

1. First: Multiply the first terms:
   $2a \times 2a = 4a^2$

2. Outer: Multiply the outer terms:
   $2a \times -3b = -6ab$

3. Inner: Multiply the inner terms:
   $-3b \times 2a = -6ab$

4. Last: Multiply the last terms:
   $-3b \times -3b = 9b^2$

Combine the terms:

Now, let's add everything together:

$4a^2 - 6ab - 6ab + 9b^2$

The two middle terms, $-6ab$ and $-6ab$, can be combined:

$4a^2 - 12ab + 9b^2$

Final simplified expression:

$(2a - 3b)^2 = 4a^2 - 12ab + 9b^2$

Summary:

• Step 1: Multiply each part (use FOIL).
• Step 2: Combine like terms.
• Step 3: The final result is $4a^2 - 12ab + 9b^2$.

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Would you like to see more details or have any questions?

Here are 5 related questions you might find helpful:

1. What happens if you square a binomial with different terms?
2. How do you apply the distributive property in binomial multiplication?
3. What is the difference between expanding and factoring?
4. How do you simplify expressions involving variables?
5. What does the middle term represent in binomial expansions?

Tip: Always combine like terms carefully after multiplying binomials!