What is factor x^3+x^{-3} ?

The solution to factor x^3+x^{-3} is ((x^2+1)(x^4-x^2+1))/(x^3)

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factor x^3+x^{-3}

factor

x^{3} + x^{- 3}

\frac{( x ^{2} + 1 ) ( x ^{4} - x ^{2} + 1 )}{x ^{3}}

Solution steps

x^{3} + x^{- 3}

Apply exponent rule:

a^{b + c} = a^{b} a^{c}

x^{3} = x^{- 3} x^{6}

= x^{- 3} x^{6} + x^{- 3}

Factor out common term

x^{- 3}

= x^{- 3} (x^{6} + 1)

Factor

x^{6} + 1 : (x^{2} + 1) (x^{4} - x^{2} + 1)

= x^{- 3} (x^{2} + 1) (x^{4} - x^{2} + 1)

Refine

= \frac{( x ^{2} + 1 ) ( x ^{4} - x ^{2} + 1 )}{x ^{3}}

2 x^{12} - 4 x^{2}

e (- 4)

a x + b y - c x + a y + b x - cy

10 e - 55

tan (3 t - 15) tan (2 t + 5)

What is factor x^3+x^{-3} ?
The solution to factor x^3+x^{-3} is ((x^2+1)(x^4-x^2+1))/(x^3)