Final answer:
To divide 2x³ * 2 - 2x⁸ by x², first simplify the equation by expanding and multiplying terms. Then, divide the terms by subtracting the exponents and dividing the coefficients. Finally, simplify the expression to obtain the result.
Step-by-step explanation:
Step 1: Simplify the equation
To simplify the equation, we expand and multiply the terms:
4x³ - 2x⁸ / x² = 4x(x²) - 2x⁶(x²), which simplifies to 4x³ - 2x⁸ = 4x³ - 2x⁸.
Step 2: Divide the terms
To divide the terms, we subtract the exponents and divide the coefficients:
4x³ - 2x⁸ / x² = (4x³) / (x²) - (2x⁸) / (x²) = 4x^(3-2) - 2x^(8-2) = 4x - 2x⁶.
Step 3: Simplify the expression
The final expression after simplification is 4x - 2x⁶.