Math Problem Statement

factor x^2 - 9

Solution

The expression x29x^2 - 9 is a difference of squares. A difference of squares is a special form that can be factored using the identity:

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

In this case, x29x^2 - 9 can be rewritten as:

x232x^2 - 3^2

Here, a=xa = x and b=3b = 3. Applying the difference of squares formula, we get:

x29=(x3)(x+3)x^2 - 9 = (x - 3)(x + 3)

So, the factored form of x29x^2 - 9 is:

(x3)(x+3)\boxed{(x - 3)(x + 3)}

Would you like further details or have any questions about this process?

Related Questions

  1. How do you factor expressions that are not perfect squares?
  2. What are some other examples of the difference of squares?
  3. How do you factor x24x+4x^2 - 4x + 4?
  4. Can the difference of cubes be factored similarly to the difference of squares?
  5. How does factoring help in solving equations?

Tip: Recognizing patterns like the difference of squares can make factoring much quicker and easier. Look for perfect squares and a subtraction sign to apply this technique effectively.

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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