Factoring Difference of Squares Math Example 3

Follow the full solution, then compare it with the other examples linked below.

Example 3

easy
Factor x2−1x^2 - 1.

Solution

  1. 1
    x2−1=x2−12=(x+1)(x−1)x^2 - 1 = x^2 - 1^2 = (x + 1)(x - 1).
  2. 2
    Check: (x+1)(x−1)=x2−1(x+1)(x-1) = x^2 - 1 ✓

Answer

(x+1)(x−1)(x + 1)(x - 1)
The simplest difference of squares: x2−1x^2 - 1 factors into (x+1)(x−1)(x+1)(x-1). Remember: a2+b2a^2 + b^2 (sum of squares) does NOT factor over the reals.

About Factoring Difference of Squares

Recognizing and factoring expressions of the form a2−b2a^2 - b^2 into the product (a+b)(a−b)(a + b)(a - b).

Learn more about Factoring Difference of Squares →

More Factoring Difference of Squares Examples

Example 1 easy

Factor [formula].

Example 2 medium

Factor [formula].

Example 4 hard

Factor [formula] completely.

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