Math Problem Statement

-2sqrt2-2sqrt2

Solution

To simplify the expression 2222-2\sqrt{2} - 2\sqrt{2}, we can combine the like terms.

Step-by-step Solution:

  1. The expression consists of two terms: 22-2\sqrt{2} and 22-2\sqrt{2}.

  2. Since both terms are similar, you can add them directly:

    2222=(22)2-2\sqrt{2} - 2\sqrt{2} = (-2 - 2)\sqrt{2}

  3. Simplify the coefficients:

    (22)=4(-2 - 2) = -4

  4. So, the simplified expression is:

    42-4\sqrt{2}

Final Answer:

2222=42-2\sqrt{2} - 2\sqrt{2} = -4\sqrt{2}

Would you like more details or have any questions?

Here are some related questions to explore:

  1. How do you simplify expressions involving square roots?
  2. What are like terms, and how can they be combined?
  3. How do you factor expressions with square roots?
  4. How can you rationalize expressions involving square roots?
  5. How do you simplify expressions with different coefficients?

Tip: Always look for like terms to combine in expressions to simplify them quickly.

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Math Problem Analysis

Mathematical Concepts

Algebra
Simplifying Radicals
Combining Like Terms

Formulas

Combining Like Terms: a√b + c√b = (a + c)√b

Theorems

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Suitable Grade Level

Grades 7-8