Math Problem Statement

Expand and simplify: (2 - 2√5) + (5 + √5)

Solution

The problem shown in the image appears to be:

Expand and simplify:
(225)+(5+5)(2 - 2\sqrt{5}) + (5 + \sqrt{5})

Step 1: Combine like terms

  • Combine the constant terms: 2+5=72 + 5 = 7
  • Combine the terms with 5\sqrt{5}: 25+5=5-2\sqrt{5} + \sqrt{5} = -\sqrt{5}

Step 2: Write the simplified expression

The result is: 757 - \sqrt{5}

Would you like further explanation or have any related questions?

Here are 5 related questions you might explore:

  1. How do you expand and simplify expressions involving square roots?
  2. What are like terms, and how do you identify them in an equation?
  3. Can you show an example with three or more terms including square roots?
  4. How do you handle expressions with nested parentheses involving radicals?
  5. Why does a+b\sqrt{a} + \sqrt{b} not simplify to a+b\sqrt{a+b}?

Tip: Always combine terms systematically to avoid missing any like terms!

Ask a new question for Free

By Image

Drop file here or Click Here to upload

Math Problem Analysis

Mathematical Concepts

Simplification of Expressions
Radicals and Square Roots
Combining Like Terms

Formulas

a√b + c√b = (a + c)√b
Simplifying expressions with square roots

Theorems

Properties of Square Roots and Like Terms

Suitable Grade Level

Grades 9-10