Factorize the expression X 4 +324. Idk how to sol

To factor the expression \(X^4 + 324\), we can recognize that it is a sum of squares. The expression can be rewritten as:

Recognizing the Sum of Squares

We can express \(324\) as \(18^2\), so the expression becomes:

\(X^4 + 18^2\)

Applying the Sum of Squares Formula

The sum of squares can be factored using the formula:

• \(a^2 + b^2 = (a + bi)(a - bi)\)

In our case, let \(a = X^2\) and \(b = 18\). Thus, we can write:

\(X^4 + 324 = (X^2 + 18i)(X^2 - 18i)\)

Final Factorization

Therefore, the factorization of \(X^4 + 324\) is:

\((X^2 + 18i)(X^2 - 18i)\)

This shows the expression in its factored form using complex numbers. If you need further assistance with real number factorizations or other concepts, feel free to ask!