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Square the expression. Write your answer in simplest form.

The expression you provided is \((-5\sqrt{21} - \sqrt{35})^2\). To square this expression, we again use the formula for the square of a binomial:

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

Here, \( a = -5\sqrt{21} \) and \( b = \sqrt{35} \).

Let's break this down:

1. \( a^2 = (-5\sqrt{21})^2 = 25 \times 21 = 525 \)
2. \( b^2 = (\sqrt{35})^2 = 35 \)
3. \( 2ab = 2(-5\sqrt{21})(\sqrt{35}) = -10\sqrt{21 \times 35} = -10\sqrt{735} \)

Combine these results:

\[
(-5\sqrt{21} - \sqrt{35})^2 = 525 + 35 - 10\sqrt{735} = 560 - 10\sqrt{735}
\]

So, the expression simplifies to:

\[
\boxed{560 - 10\sqrt{735}}
\]

Would you like more details or have any further questions?

### Related Questions:
1. How do you handle squaring expressions with negative signs and radicals?
2. What is the importance of simplifying square roots before or after squaring?
3. How would you simplify the expression \(\sqrt{735}\)?
4. What would be the steps to solve \((-2\sqrt{11} + \sqrt{7})^2\)?
5. Can binomial expansion be applied to complex numbers with square roots?
6. How does the squaring process differ for sums and differences of radicals?
7. What are some common pitfalls when dealing with square roots in algebraic expressions?
8. How is this problem similar to finding the area of a square with irrational side lengths?

### Tip:
Always keep track of negative signs when squaring expressions, as they can significantly alter the final result.

Learn how to square the expression -5√21 - √35 with a step-by-step solution in simplest form. This problem involves applying the binomial square formula and simplifying radicals. Suitable for high school students.

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