Question

How do we solve for (∛x-1)(∛x+1)?

Answer 1

What you have shown is not an equation, so you cannot solve for the value of x.
Without the equal sign, what is shown is an expression, which can be simplified using the identity:
\((a+b)(a-b)=a^2-b^2\)
where in the particular case, a=\(x^\frac{1}{3}\), and b=1.
Use also the following rule of exponents to simplify \(a^2.\)
\((a^x)^2=a^{2x}\)