# How do you multiply (x^(1/3) + x^(-1/3))^2?

Feb 14, 2016

${x}^{\frac{2}{3}} + {x}^{- \frac{2}{3}} + 2$

#### Explanation:

making use of the laws of exponents :

• a^m xx a^n = a^(m+n)

• a^0 = 1

then ${\left({x}^{\frac{1}{3}} + {x}^{- \frac{1}{3}}\right)}^{2} = \left({x}^{\frac{1}{3}} + {x}^{- \frac{1}{3}}\right) \left({x}^{\frac{1}{3}} + {x}^{- \frac{1}{3}}\right)$

distribute the brackets using FOIL (or any method you have)

$= {x}^{\frac{1}{3}} \times {x}^{\frac{1}{3}} + {x}^{- \frac{1}{3}} \times {x}^{\frac{1}{3}} + {x}^{- \frac{1}{3}} \times {x}^{\frac{1}{3}} + {x}^{- \frac{1}{3}} \times {x}^{- \frac{1}{3}}$
( using the above laws to simplify )

$= {x}^{\frac{2}{3}} + {x}^{0} + {x}^{0} + {x}^{- \frac{2}{3}}$

$= {x}^{\frac{2}{3}} + 1 + 1 + {x}^{- \frac{2}{3}} = {x}^{\frac{2}{3}} + 2 + {x}^{- \frac{2}{3}}$