Factor completely:

\[ x^4 - 81 \]

x 4 − 81 = ( x 2 − 9 ) ( x 2 + 9 ) = ( x − 3 ) ( x + 3 ) ( x 2 + 9 )

Answered by konrad509 | 2024-06-10

The expression x 4 − 81 can be factored as ( x − 3 ) ( x + 3 ) ( x 2 + 9 ) . The first two factors come from recognizing it as a difference of squares, while x 2 + 9 cannot be factored further over the reals. Thus, this is the complete factorization.
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Answered by konrad509 | 2024-12-26