Answers

2016-06-25T10:43:01+08:00

We can simply multiply it by itself three times but we can also simply do this instead:


(a + b)³ = a³ + 3a²b + 3ab² + b³
(a - b)³  = a³ + 3a²b + 3ab² + b³     
(but since the operation used is subtraction, at the end it'll look like this: a³ - 3a²b + 3ab² - b³ but it's just the same, anyway.)

The cube of the square of the binomial is equal to the cube of the first term plus three multiplied to the product of the square of the first term and the second term plus three multiplied to the product of the first term and square of the second term plus the cube of the second term.
Ex.:
(3x + 9) = (3x)³ + 3(3x)²(9) + 3(3x)(9)² + (9)³
             = 27x³ +   243x²    +    729x    + 729

(5m - 17) = (5m)³ + 3(5m)²(-17) + 3(5m)(17)² + (-17)³
                =125m³  + (-1275m²)  +  4335m      + (-4913)
                = 125m³ - 1275m² + 4335m - 4913
0