Universalka

Verified answer

1) (2a-b)⁵ = (2a)⁵ - 5(2a)⁴b + 10(2a)³b² - 10(2a)²b³ + 5(2a)b⁴ - b⁵ =  32a⁵ - 80a⁴b + 80a³b² - 40a²b³ + 10ab⁴ - b⁵
2) (x - 2y)⁵ = x⁵ - 5x⁴(2y) + 10x³(2y)² - 10x²(2y)³ + 5x(2y)⁴ - (2y)⁵ =
= x⁵ - 10x⁴y + 40x³y² - 80x²y + 80xy⁴ - 32y⁵
3) (1/2 - √2)⁶ = (1/2)⁶ - 6(1/2)⁵ √2 + 15(1/2)⁴(√2)² - 20(1/2)³(√2)³ + 15(1/2)²(√2)⁴ -6(1/2)(√2)⁵ + (√2)⁶ = 1/64 -3/16√2 + 15/8 - 5√2 + 15 -
- 12√2 + 16
4) (√3 - 1/3)⁶ =(√3) ⁶ - 6(√3)⁵*1/3 + 15(√3)⁴ *(1/3)² - 20(√3)³ * (1/3)³ + 15(√3)² *(1/3)⁴ - 6(√3)*(1/3)⁵ + (√3)⁶  = 27 - 18√3 + 15 - 20√3/3 + 5/9 - 2√3/81 + 27
5)(x - 1/2x)⁷ = x⁷ - 7x⁶ *(1/2x) + 21x⁵(1/2x)² - 35x⁴(1/2x)³ + 35x³(1/2x)⁴ - 21x²(1/2x)⁵ + 7x(1/2x)⁶- (1/2x)⁷ = x⁷ -7/2 x⁷ + 21/4x⁷ - 35/8x⁷ + 35/16x⁷ - 21/32x⁷ + 7/64x⁷- 1/128x⁷
6) (1/2y - y)⁸ = (1/2y)⁸ - 8(1/2y)⁷y + 28(1/2y)⁶y² - 56(1/2y)⁵y³ + 70(1/2y)⁴y⁴-
-56(1/2y)³y⁵ + 28(1/2y)²y⁶ - 8(1/2y)y⁷ + y⁸ = 1/256y⁸ - 1/16y⁸ + 7/16y⁸ -
- 7/4y⁸ + 35/8y⁸ - 7y⁸ + 7y⁸ - 4y⁸ + y⁸
1) (2a -b)⁵ = C₅⁰(2a)⁵ - C₅¹(2a)⁴b + C₅²(2a)³b² - C₅³(2a)⁴b³ + C₅⁴(2a)⁵b⁴ - C₅⁵b⁵