How can you factor x^4 +1?
I need to factor by difference of squares. How can I do this?
change it to
x^4 - (sqrt(-1))^2 or
x^4 - i^2
To factor x^4 + 1 using the difference of squares method, you need to rewrite it in the form of a perfect square minus another perfect square. In this case, you can rewrite it as x^4 - (i^2), where i represents the imaginary unit equal to the square root of -1.
Now, recall that i^2 is equal to -1. Substituting this value, the expression becomes x^4 - (-1) or x^4 + 1.
Since x^4 - (-1) is in the form of a difference of squares, it can be factored as the product of a sum and difference. Using this form, you can factor:
x^4 + 1 = (x^2)^2 - i^2
By applying the difference of squares formula: a^2 - b^2 = (a+b)(a-b), where a = x^2 and b = i, we can factor the expression further:
= (x^2 + i)(x^2 - i)
So, the factored form of x^4 + 1 using the difference of squares method is (x^2 + i)(x^2 - i).