To expand \((8x - 5y)(8x - 5y)\), we can apply the formula for squaring a binomial, which is:

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

Here, \(a = 8x\) and \(b = 5y\). Using the formula:

\[
(8x - 5y)^2 = (8x)^2 - 2(8x)(5y) + (5y)^2
\]

Now calculate each term:

- \((8x)^2 = 64x^2\)
- \(-2(8x)(5y) = -80xy\)
- \((5y)^2 = 25y^2\)

So the expanded form is:

\[
64x^2 - 80xy + 25y^2
\]

Would you like further details on any part of this expansion?

Here are 5 related questions for practice:
1. What is the expanded form of \((7x - 2y)^2\)?
2. How would you expand \((3x + 4y)(3x + 4y)\)?
3. What is the result of expanding \((9x + 6y)^2\)?
4. How does the expansion change if both terms are positive, e.g., \((5x + 7y)(5x + 7y)\)?
5. Can you use the distributive property to expand \((6x - y)(6x + y)\)?

**Tip:** When expanding binomials, remember to carefully apply the distributive property to avoid sign errors.

Learn how to expand the binomial expression (8x - 5y)(8x - 5y) step by step using the formula for squaring a binomial. This solution breaks down key algebraic concepts, such as polynomials and binomial expansion, making it suitable for students in Grades 8-10.

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