To expand \( (4x - 3y)^2 \), we can use the formula for squaring a binomial:

\[
(a - b)^2 = a^2 - 2ab + b^2
\]

In this case:
- \( a = 4x \)
- \( b = 3y \)

Now, apply the formula:

\[
(4x - 3y)^2 = (4x)^2 - 2(4x)(3y) + (3y)^2
\]

First, calculate each term:
- \( (4x)^2 = 16x^2 \)
- \( 2(4x)(3y) = 24xy \)
- \( (3y)^2 = 9y^2 \)

Putting it all together:

\[
(4x - 3y)^2 = 16x^2 - 24xy + 9y^2
\]

So, the expanded form is:

\[
16x^2 - 24xy + 9y^2
\]

Would you like more details or have any questions?

Here are 5 related questions to explore:
1. What happens when you expand \( (4x + 3y)^2 \)?
2. Can you apply the same method to \( (5x - 2y)^2 \)?
3. How do you factor \( 16x^2 - 24xy + 9y^2 \) back to the original form?
4. What is the general formula for expanding \( (ax - by)^2 \)?
5. How does the expansion change if the expression is \( (4x - 3y)^3 \)?

**Tip:** When squaring binomials, always double-check each intermediate term to avoid sign errors!

Learn how to expand the expression (4x - 3y)² using binomial expansion. This step-by-step solution demonstrates key algebraic concepts, including polynomial operations and the binomial theorem. Perfect for students in Grades 8-10.

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