Final answer:
The problem involves expanding a squared binomial and simplifying the expression to compare it with another polynomial. The steps include using the FOIL method, combining like terms, and finding solutions that satisfy the equation.Step-by-step explanation:
The question pertains to the simplification of a mathematical expression and involves understanding the process of expanding and manipulating exponents and polynomial expressions. The steps to simplify the equation (2x⁻⁴ - y³)² = (3x⁶ - y²) would include expanding the squared binomial on the left side and then comparing or solving for the variables with the equation on the right side. Let's outline the steps:1. Expand the binomial (2x⁻⁴ - y³)² using the FOIL method (First, Outer, Inner, Last).2. Simplify the expressions obtained from the expansion by combining like terms, if available.3. Compare the resulting expression with the right-hand side equation (3x⁶ - y²).4. Look for possible solutions that satisfy both sides of the original equation, or determine if more information is needed to solve for x and y.