Math Problem Statement

FACTOR 16x^2-1

Solution

The expression 16x2116x^2 - 1 can be factored as a difference of squares. The difference of squares formula is:

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

Here, we can identify 16x216x^2 as (4x)2(4x)^2 and 11 as 121^2. Applying the formula:

16x21=(4x)212=(4x1)(4x+1)16x^2 - 1 = (4x)^2 - 1^2 = (4x - 1)(4x + 1)

So, the factored form of 16x2116x^2 - 1 is:

(4x1)(4x+1)(4x - 1)(4x + 1)

Would you like more details or have any questions? Here are some related questions you might find helpful:

  1. How do you factor a trinomial?
  2. What is the difference of cubes formula?
  3. How can you check if a quadratic expression is factorable?
  4. What is the significance of the discriminant in factoring?
  5. How do you solve quadratic equations by factoring?

Tip: Always look for common factors before applying special factoring formulas like the difference of squares.

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Math Problem Analysis

Mathematical Concepts

Algebra
Factoring
Quadratic Equations

Formulas

Difference of squares

Theorems

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Suitable Grade Level

Grades 9-12