Verified answer

используем a² - b² = (a - b)(a + b)

(x³ - 9y⁴)² - (x³ + 9y⁴)²  - 36x³(y⁴ - x) = (x³ - 9y⁴  - x³ - 9y⁴)(x³ - 9y⁴  + x³ + 9y⁴) - 36x³y⁴ + 36x⁴ = - 18y⁴*2x³ + 36x³y⁴ - 36x⁴ =  -36x³y⁴+ 36x³y⁴ - 36x⁴ = -36x⁴ доказано

0.5z⁴(40zt² - 5) - (z⁵ + 10t²)² + (10t² - z⁵)² = (10t² - z⁵ - z⁵ - 10t²)(10t² - z⁵ + z⁵ + 10t²) + 20z⁵t² - 2.5z⁴ = -2z⁵*20t² + 20z⁵t² - 2.5z⁴ = -40z⁵t² + 20z⁵t² - 2.5z⁴ = - 20z⁵t² - 2.5z⁴ доказано