Express the product left parenthesis, square root of, 5, end square root, minus, 7, right parenthesis, left parenthesis, square root of, 5, end square root, minus, 7, right parenthesis( 
5
​
 −7)( 
5
​
 −7) in simplest form.

We are tasked with simplifying the product of \((\sqrt{5} - 7)(\sqrt{5} - 7)\). This expression represents the square of the binomial \(\sqrt{5} - 7\).

We can apply the **square of a binomial** formula:
\[
(a - b)^2 = a^2 - 2ab + b^2
\]
Here, \(a = \sqrt{5}\) and \(b = 7\). Let's expand this using the formula:

\[
(\sqrt{5} - 7)^2 = (\sqrt{5})^2 - 2(\sqrt{5})(7) + 7^2
\]

Now, compute each part:

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

Thus, the expression becomes:
\[
5 - 14\sqrt{5} + 49
\]

Combine like terms:
\[
5 + 49 - 14\sqrt{5} = 54 - 14\sqrt{5}
\]

So, the simplest form of the expression is:
\[
54 - 14\sqrt{5}
\]

Would you like more details or have any questions?

Here are five related questions you might find helpful:
1. How do you expand the square of a binomial when there are different radicals?
2. What are the steps to simplify an expression involving radicals?
3. Can the expression \(54 - 14\sqrt{5}\) be simplified further?
4. What happens when you multiply binomials that have different radical terms?
5. How does the distributive property relate to expanding binomials?

**Tip:** Always combine like terms carefully after expanding binomials to simplify expressions correctly!

Express the product (sqrt(5) - 7)(sqrt(5) - 7) in simplest form.

This guide explains how to simplify the product (sqrt(5) - 7)(sqrt(5) - 7) using the square of a binomial formula. Learn key concepts in algebra and radicals, with step-by-step explanations. Suitable for Grades 9-10 students.

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