Factor x^2-1
Factor polynomials completely: trinomials, difference of squares, sum/difference of cubes.
To factor x^2-1, recognize this as a difference of two squares — a² − b² = (a + b)(a − b).
x2-1
This expression has two terms connected by subtraction, and both are perfect squares. This matches the difference of squares pattern.
The identity states:
a2 − b2 = (a + b)(a − b)
Identify a and b:
a = x (since (x)2 gives the first term)
b = 1 (since 12 = 1)
Substitute a and b into (a + b)(a − b):
= (x + 1)(x − 1)
(x - 1)(x + 1)
How to factor x^2-1
To factor x^2-1, identify the type of polynomial and apply the appropriate technique. The factored form is (x - 1)(x + 1).
This is a polynomial factoring problem — we break a polynomial into a product of simpler expressions. Common methods include GCF extraction, difference of squares, and trinomial factoring.
Frequently asked questions
What is the answer to x^2-1?
The answer is (x - 1)(x + 1).
What method is used?
identifying the polynomial type and applying the matching technique — GCF, trinomial factoring, difference of squares, or special cube formulas.