Question

Find the product of the following binomial: \[\left( x^3 + \frac{1}{x^3} \right)\left( x^3 - \frac{1}{x^3} \right)\]

Answer 1

 We will use the identity

\[\left( a + b \right)\left( a - b \right) = a^2 - b^2\] in the given expression to find the product.

\[\left( x^3 + \frac{1}{x^3} \right)\left( x^3 - \frac{1}{x^3} \right)\]

\[ = \left( x^3 \right)^2 - \left( \frac{1}{x^3} \right)^2 \]

\[ = x^6 - \frac{1}{x^6}\]