How can you factor x^4 +1?
If you go to the imaginary plane, it factors to
(x^2 + i)(x^2-i)
I need to factor by difference of squares. How can I do this?
To factor the expression x^4 + 1, you can use the difference of squares formula. However, it's important to note that the given expression cannot be factored using real numbers only. The factorization that you mentioned involving the imaginary unit 'i' is indeed correct.
In the imaginary plane, the expression factors as (x^2 + i)(x^2 - i).
Now, if you want to proceed with factoring by difference of squares, you need to consider complex numbers. The difference of squares formula states that a^2 - b^2 can be factored as (a + b)(a - b).
But, since we're dealing with an expression involving the imaginary unit 'i', we can rewrite 'i^2' as -1.
So, x^4 + 1 can be written as (x^4 + i^2).
Now, applying the difference of squares formula, we have:
(x^2 + i)(x^2 - i)
This is the factored form of x^4 + 1 in the complex number system, using the difference of squares technique.