Math Problem Statement

factor 2 - x^2

Solution

The expression 2x22 - x^2 can be factored using the difference of squares formula. The difference of squares states that:

a2b2=(ab)(a+b)a^2 - b^2 = (a - b)(a + b)

In this case, you can rewrite 2x22 - x^2 as:

2x2=22x22 - x^2 = \sqrt{2}^2 - x^2

Now, applying the difference of squares formula:

2x2=(2x)(2+x)2 - x^2 = (\sqrt{2} - x)(\sqrt{2} + x)

So, the factorization of 2x22 - x^2 is:

(2x)(2+x)(\sqrt{2} - x)(\sqrt{2} + x)

Would you like more details, or do you have any other questions?


Here are some related questions you might find useful:

  1. How do you recognize when to use the difference of squares formula?
  2. Can the expression 2x22 - x^2 be factored further?
  3. How do you factor expressions like 2x282x^2 - 8?
  4. What are the roots of the equation 2x2=02 - x^2 = 0?
  5. How can you solve quadratic equations by factoring?
  6. What is the geometric interpretation of the difference of squares?
  7. How do you factor more complex quadratic expressions?
  8. Can difference of squares be applied to higher-degree polynomials?

Tip: When dealing with a quadratic expression, always check if it can be rewritten as a difference of squares—it’s a common and useful factoring technique.

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Math Problem Analysis

Mathematical Concepts

Algebra
Quadratic Equations
Difference of Squares

Formulas

Difference of squares formula

Theorems

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Suitable Grade Level

Grades 10-12