Serena presented the following solution to show that the following equation (where i is the imaginary unit) is NOT an identity. x^{3} + 25x = x(x + 5i)(x - 5i)

STEP 1:

x^{3} + 25x

= x(x^{2} + x5i - x5i - 25i^{2})

STEP 2:

= x(x^{2} + 25i^{2})

STEP 3:

= x^{3} + 25i^{2}x

STEP 4:

= x^{3} - 25x Not an identity!

Is her solution correct? If not, in which step did she make her error?

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