cube of a binomial:
(x + y)³ = x³ + 3x²y + 3xy² + y³
1.) (x + 4)³ = (x)³ + 3(x)²(4) + 3(x)(4)² + (4)³
(x)³ = x³
3(x)²(4) = 12x²
3(x)(4)² = 48x
(4)³ = 64
x³ + 12x² + 48x + 64
2.) (2x + 3)³ = (2x)³ + 3(2x)²(3) + 3(2x)(3)² + (3)³
(2x)³ = 8x³
3(2x)²(3) = 36x²
3(2x)(3)² = 54x
(3)³ = 27
8x³ + 36x² + 54x + 27
3.) (4m - 3n)³ = (4m)³ - 3(4m)²(3n) + 3(4m)(3n)² - (3n)³
(4m)³ = 64m³
- 3(4m)²(3n) = -144m²n
3(4m)(3n)² = 108mn²
- (3n)³ = -27n³
64m³ - 144m²n + 108mn² - 27n³
4.) (3a - 2b)³ = (3a)³ - 3(3a)²(2b) + 3(3a)(2b)² - (2b)³
(3a)³ = 27a³
- 3(3a)²(2b) = -54a²b
3(3a)(2b)² = 36ab²
- (2b)³ = -8b³
27a³ - 54a²b + 36ab² - 8b³
5.) (x²y + 2z³)³ = (x²y)³ + 3(x²y)²(2z³) + 3(x²y)(2z³)² + (2z³)³
(x²y)³ = x⁶y³
3(x²y)²(2z³) = 6x⁴y²z³
3(x²y)(2z³)² = 12x²yz⁶
(2z³)³ = 8z⁹
x⁶y³ + 6x⁴y²z³ + 12x²yz⁶ + 8z⁹
