Find 2x² - 2z⁴ + y² - x² + z⁴ if x = -4, y = 3, and z = 2.

Solution:

Given:

Equation is 2x² - 2z⁴ + y² - x² + z⁴

⇒ Sorting the like terms and solving,

= (2x² - x²) + y² + (- 2z⁴ + z⁴)

= x² + y² - z⁴

Substituting x = -4, y = 3, and z = 2, we get

(-4)² + 32 - 24

16 + 9 - 16 = 9

Hence, required number is 9.

Find 2x² - 2z⁴ + y² - x² + z⁴ if x = -4, y = 3, and z = 2.

Summary:

The value of the equation, 2x² - 2z⁴ + y² - x² + z⁴ if x = -4, y = 3, and z = 2 is 9.