Math Problem Statement

Factor completely. 16x^2 - 121

Solution

The given expression is:

16x212116x^2 - 121

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

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

Here, 16x216x^2 is the square of 4x4x, and 121121 is the square of 1111. Therefore, we can rewrite the expression as:

(4x11)(4x+11)(4x - 11)(4x + 11)

Thus, the factored form of 16x212116x^2 - 121 is:

(4x11)(4x+11)(4x - 11)(4x + 11)

Would you like further clarification or details on any step? Here are some related questions you might find useful:

  1. How do you recognize a difference of squares?
  2. What are some other examples of factoring differences of squares?
  3. Can the difference of squares technique be used for higher powers?
  4. What happens when the terms in a difference of squares have coefficients that aren't perfect squares?
  5. How does factoring help in solving quadratic equations?

Tip: Whenever you're factoring an expression, always check for a greatest common factor (GCF) first before applying special factoring formulas like the difference of squares.

Ask a new question for Free

By Image

Drop file here or Click Here to upload

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 8-10