The given expression is:

$(\sqrt{5} - 7)(\sqrt{5} - 7)$

This is a binomial multiplication of the form $(a - b)(a - b)$, which can be expanded using the formula for a perfect square trinomial:

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

Here, $a = \sqrt{5}$ and $b = 7$. Let's expand it step by step:

1. Square the first term: $a^2 = (\sqrt{5})^2 = 5$

2. Multiply the two terms and then double the result: $-2ab = -2(\sqrt{5})(7) = -14\sqrt{5}$

3. Square the second term: $b^2 = 7^2 = 49$

Now, combine all the terms:

$(\sqrt{5} - 7)^2 = 5 - 14\sqrt{5} + 49$

Simplify:

$5 + 49 - 14\sqrt{5} = 54 - 14\sqrt{5}$

Thus, the product $(\sqrt{5} - 7)(\sqrt{5} - 7)$ simplifies to:

$54 - 14\sqrt{5}$

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

Here are 5 related questions:

1. How would you expand $(\sqrt{2} - 3)(\sqrt{2} - 3)$?
2. Can you explain how the perfect square trinomial formula is derived?
3. How do we handle square roots when simplifying expressions?
4. What is the difference between expanding a binomial and factoring it?
5. How can we verify the result using another method?

Tip: When expanding binomials, it's helpful to memorize the perfect square formula for quick simplification.