https://file.aiquickdraw.com/mathbot/file/172788187052881r48jfe.jpg

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.

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

This page explains how to simplify the expression (√5 - 7)(√5 - 7) using binomial expansion. Follow a step-by-step breakdown of the perfect square trinomial formula, ideal for students in Grades 8-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation