Math Problem Statement

x² - 100

Solution

The expression x2100x^2 - 100 can be factored using the difference of squares formula. The difference of squares formula states that:

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

In this case, x2x^2 is a2a^2 and 100 is b2b^2, where b=10b = 10. So, the expression can be factored as:

x2100=(x10)(x+10)x^2 - 100 = (x - 10)(x + 10)

Would you like more details or have any questions?

Here are 5 related questions:

  1. How would you factor x2144x^2 - 144?
  2. What are the roots of the equation x2100=0x^2 - 100 = 0?
  3. How can the difference of squares be used to simplify x416x^4 - 16?
  4. What happens if you try to factor x2+100x^2 + 100?
  5. How would you expand (x10)(x+10)(x - 10)(x + 10) to verify the factorization?

Tip: Always look for patterns like the difference of squares when factoring quadratic expressions.

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Math Problem Analysis

Mathematical Concepts

Algebra
Quadratic Equations
Difference of Squares

Formulas

Difference of squares formula: a^2 - b^2 = (a - b)(a + b)

Theorems

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Suitable Grade Level

Grades 7-9