The problem given is to calculate:

$(\sqrt{10} - \sqrt{7}) \cdot (\sqrt{10} + \sqrt{7})$

This is a difference of squares formula, which states:

$(a - b)(a + b) = a^2 - b^2$

In this case:

• $a = \sqrt{10}$
• $b = \sqrt{7}$

Now applying the formula:

$(\sqrt{10} - \sqrt{7}) \cdot (\sqrt{10} + \sqrt{7}) = (\sqrt{10})^2 - (\sqrt{7})^2$

This simplifies to:

$10 - 7 = 3$

Thus, the result is $3$.

Would you like more details or have any questions?

Here are 5 related questions:

1. What is the difference of squares formula?
2. How can you expand a binomial like $(a + b)(a - b)$?
3. What happens if you apply this to complex numbers?
4. Can you apply the same concept to cubes instead of squares?
5. How does the difference of squares apply to higher-order polynomials?

Tip: The difference of squares is a powerful tool in simplifying expressions and solving equations! Always look for patterns like $a^2 - b^2$.