\(factor \ x^5-81x\)
\(The \ Greatest \ Common \ Factor \ (GCF) \ is \ x\)
\(Factor \ out \ the \ GCF\)
\(x( \dfrac{x^5}{x} + \dfrac{-18x}{x})\)
\(x(x^4-81)\) \(Simplify \ each \ term \ in \ parentheses\)
\(Rewrite \ it \ where \ a=x^2 \ and \ b=9\)
\(x((x^2)2-9^2)\)
\(Use \ Difference \ of \ Squares : a^2-b^2=(a+b)(a-b)\)
\(x(x^2+9)(x^2-9)\)
\(Rewrite \ it \ where \ a=x \ and \ b=3\)
\(x(x^2+9)(x^2-3^2)\)
\(Use \ Difference \ of \ Squares : a^2-b^2=(a+b)(a-b)\)
\(x(x^2+9)(x+3)(x-3)\)
