Math Problem Statement

Factor 4x^2 - 9

Solution

The expression in the image is:

4x294x^2 - 9

This is a difference of squares, which can be factored using the identity:

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

Here, a2=4x2a^2 = 4x^2 and b2=9b^2 = 9. Therefore, we can rewrite it as:

(2x)232(2x)^2 - 3^2

Applying the difference of squares formula:

4x29=(2x3)(2x+3)4x^2 - 9 = (2x - 3)(2x + 3)

Thus, the factored form of the expression is:

(2x3)(2x+3)(2x - 3)(2x + 3)

Let me know if you'd like further details or explanations.

Here are some related questions:

  1. What is the general method for factoring a quadratic expression?
  2. Can all quadratic expressions be factored using the difference of squares method?
  3. How do you factor other types of binomials, like perfect square trinomials?
  4. What is the process for factoring quadratics that cannot be factored easily?
  5. How does factoring help in solving quadratic equations?

Tip: Always check if the expression fits a common factoring pattern, such as the difference of squares or perfect square trinomials, to make factoring easier.

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Math Problem Analysis

Mathematical Concepts

Algebra
Factoring
Difference of Squares

Formulas

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

Theorems

Difference of Squares Theorem

Suitable Grade Level

Grades 7-10