Factor [tex]x^{2}[/tex] + 64

Factor [tex]x^{2}[/tex] + 64

The expression x^2 + 64 is a quadratic expression that cannot be factored using real numbers. However, it can be factored using complex numbers.

We know that i^2 = -1, so we can write:

x^2 + 64 = x^2 - (-64)

Now, we can use the difference of squares formula, which states that:

a^2 - b^2 = (a + b)(a - b)

Using this formula, we can write:

x^2 + 64 = (x + 8i)(x - 8i)

Therefore, the factored form of x^2 + 64 is (x + 8i)(x - 8i).

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