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Let's solve the given expression \((\sqrt{10} - \sqrt{7})(\sqrt{10} - \sqrt{7})\), which is a product of two binomials.

This expression can be rewritten as:
\[
(\sqrt{10} - \sqrt{7})^2
\]
Now, expand this binomial using the formula \((a - b)^2 = a^2 - 2ab + b^2\), where \(a = \sqrt{10}\) and \(b = \sqrt{7}\):

\[
(\sqrt{10})^2 - 2(\sqrt{10})(\sqrt{7}) + (\sqrt{7})^2
\]

Now, simplify each term:

1. \((\sqrt{10})^2 = 10\)
2. \((\sqrt{7})^2 = 7\)
3. \(2(\sqrt{10})(\sqrt{7}) = 2\sqrt{70}\)

Thus, the expression becomes:
\[
10 - 2\sqrt{70} + 7
\]

Finally, combine like terms:
\[
17 - 2\sqrt{70}
\]

So, the simplified form of the given product is:
\[
17 - 2\sqrt{70}
\]

Would you like more details on any specific step, or do you have any further questions?

Here are some related questions:
1. How would you handle a similar expression with addition, such as \((\sqrt{10} + \sqrt{7})(\sqrt{10} + \sqrt{7})\)?
2. What is the general formula for the difference of squares, and how could it apply here?
3. How do you multiply expressions involving square roots?
4. Can this result be simplified further if approximations for square roots are used?
5. How would you handle expressions like \((\sqrt{a} - \sqrt{b})(\sqrt{a} + \sqrt{b})\)?

**Tip**: When simplifying radical expressions, always check if further simplifications (like combining square roots or rationalizing) are possible.

Express the product (√10 - √7)(√10 - √7) in simplest form.

Learn how to simplify the product (√10 - √7)(√10 - √7) by expanding and applying binomial expansion rules. This problem covers key concepts like radicals and binomial squares, suitable for students in Grades 9-11.

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