Start by squaring the expression within the parentheses (3y^-1 - x^-2)^2 = (3y^-1 - x^-2)(3y^-1 - x^-2 Expanding this using the distributive property = 9y^-2 - 3y^-1x^-2 - 3x^-2y^-1 + x^-4
Now plug this back into the original expression 6x^-2y^-1 + (9y^-2 - 3y^-1x^-2 - 3x^-2y^-1 + x^-4)
Let's simplify the given expression step by step.
Start by squaring the expression within the parentheses
(3y^-1 - x^-2)^2 = (3y^-1 - x^-2)(3y^-1 - x^-2
Expanding this using the distributive property
= 9y^-2 - 3y^-1x^-2 - 3x^-2y^-1 + x^-4
Now plug this back into the original expression
6x^-2y^-1 + (9y^-2 - 3y^-1x^-2 - 3x^-2y^-1 + x^-4)
Simplify by combining like terms
6x^-2y^-1 + 9y^-2 - 3y^-1x^-2 - 3x^-2y^-1 + x^-
= 9y^-2 + 6x^-2y^-1 - 3y^-1x^-2 - 3x^-2y^-1 + x^-4
Therefore, the simplified expression is 9y^-2 + 6x^-2y^-1 - 3y^-1x^-2 - 3x^-2y^-1 + x^-4.