x^2+225 ... factor expression over the complex numbers?
To factor the expression x^2 + 225 over the complex numbers, we can use the fact that the sum of two squares can be factored into complex conjugate pairs.
The given expression x^2 + 225 can be written as (x^2 + 15^2), which is in the form of a sum of squares.
Using the identity a^2 - b^2 = (a + b)(a - b), we can rewrite the expression as:
x^2 + 15^2 = (x + 15i)(x - 15i)
Therefore, the expression x^2 + 225 can be factored over the complex numbers as (x + 15i)(x - 15i).
To factor the expression x^2 + 225 over the complex numbers, we can use the difference of squares formula. However, first we need to rewrite the expression as (x^2 - (-15^2)).
Now, applying the difference of squares formula, we have:
x^2 - a^2 = (x - a)(x + a)
In this case, a is equal to 15. Therefore, we can factor the expression as follows:
x^2 + 225 = (x - 15)(x + 15)
So, the factored form of the expression x^2 + 225 over the complex numbers is (x - 15)(x + 15).