Question

Find the product (in simplified form). x²y - z² x 2y² - z² x 2y - 2²

Answer 1

To find the product of x²y - z² multiplied by 2y² - z² multiplied by 2y - 2², multiply each term using the distributive property and simplify the expression. Combine like terms to get the final simplified product: -4x²y³z² + 12y³z² - 6y²z⁴.

Step-by-step explanation:

To find the product of x²y - z² multiplied by 2y² - z² multiplied by 2y - 2², we can multiply each term using the distributive property and simplify the expression. First, multiply each term:

1. x²y x 2y² x 2y = 4x²y³
2. x²y x 2y² x -z² = -2x²y³z²
3. -z² x 2y² x 2y = -4y³z²
4. -z² x 2y² x -z² = 2y²z⁴
5. x²y x -2² x 2y = -8x²y³
6. x²y x -2² x -z² = 4x²y³z²
7. -z² x -2² x 2y = 16y³z²
8. -z² x -2² x -z² = -8y²z⁴

Then, combine like terms by adding or subtracting terms with the same variables raised to the same powers:

4x²y³ - 2x²y³z² - 4y³z² + 2y²z⁴ - 8x²y³ + 4x²y³z² + 16y³z² - 8y²z⁴

Finally, simplify the expression by combining like terms again:

-4x²y³z² + 12y³z² - 6y²z⁴

Learn more about Multiplying polynomials