https://file.aiquickdraw.com/mathbot/file/1726628253915c6iyf6ri.jpg

The expression shown in the image is:

\[
-2\sqrt{7} \left( 7 - 2\sqrt{14} \right)
\]

Let's break this down and simplify it step-by-step.

### Step 1: Distribute \(-2\sqrt{7}\) into the parentheses
Apply the distributive property:
\[
-2\sqrt{7} \times 7 - 2\sqrt{7} \times (-2\sqrt{14})
\]

This simplifies to:
\[
-14\sqrt{7} + 4\sqrt{7} \sqrt{14}
\]

### Step 2: Simplify \(\sqrt{7} \sqrt{14}\)
Since \(\sqrt{14} = \sqrt{7 \times 2} = \sqrt{7} \times \sqrt{2}\), we get:
\[
\sqrt{7} \sqrt{14} = \sqrt{7} \times \sqrt{7} \times \sqrt{2} = 7\sqrt{2}
\]

### Step 3: Substitute into the expression
Now, we substitute \(\sqrt{7} \sqrt{14} = 7\sqrt{2}\) into the equation:
\[
-14\sqrt{7} + 4 \times 7\sqrt{2}
\]

Simplify this further:
\[
-14\sqrt{7} + 28\sqrt{2}
\]

### Final Answer
The simplified form of the given expression is:
\[
-14\sqrt{7} + 28\sqrt{2}
\]

Would you like further details or have any questions?

Here are some related questions to expand on this topic:
1. How do you multiply two square roots with different radicands?
2. What is the distributive property in algebra, and how is it used here?
3. How can we further simplify expressions involving square roots?
4. How do you combine like terms in expressions with square roots?
5. What are the rules for simplifying radicals?

**Tip:** When dealing with square roots, it's helpful to factor numbers inside the square root to see if they can be broken down further. This can make simplification easier.

This problem involves simplifying the expression -2√7(7 - 2√14). Learn how to apply the distributive property, simplify square roots, and combine like terms in this detailed step-by-step solution. Suitable for students in Grades 9-11.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation