Factor completely: c^4 - 1
(c^2 - 1)(c^2 + 1)
(c - 1)(c + 1)(c^2 + 1)
To factor the expression c^4 - 1 completely, we can start by looking for any patterns or identities that can help us simplify the expression.
In this case, we can notice that the given expression is a difference of squares. The difference of squares identity states that a^2 - b^2 can be factored as (a - b)(a + b).
Applying this identity to the given expression, we can rewrite it as (c^2)^2 - 1^2.
Now we have a^2 - b^2 form, where a = c^2 and b = 1. Using the difference of squares identity, the expression can be factored as:
(c^2 - 1)(c^2 + 1)
The factors are now (c^2 - 1) and (c^2 + 1). However, we can still factor the first factor (c^2 - 1) further, as it is also a difference of squares.
Again, applying the difference of squares identity, we have:
(c - 1)(c + 1)(c^2 + 1)
So, the completely factored form of c^4 - 1 is (c - 1)(c + 1)(c^2 + 1).