Question

WHAT IS X³-27 SIMPLIFIED

Answer 1

It is (x - 3)³ - 9x(3 - x)

Explanation:

Express 27 in terms of cubes, 27 = 3³:

`= {x}^(3) - {3}^(3)`

From trinomial expansion:

`{(x - y)}^(3) = (x - y)(x - y)(x - y) \\`

open first two brackets to get a quadratic equation:

`{(x - y)}^(3) = ( {x}^(2) - 2xy + {y}^(2) )(x - y)`

expand further:

`{(x - y)}^(3) = {x}^(3) - y {x}^(2) - 2y {x}^(2) + 2x {y}^(2) + x {y}^(2) - {y}^(3) \\ {(x - y)}^(3) = {x}^(3) - {y}^(3) + 3x {y}^(2) - 3y {x}^(2) \\ {(x - y)}^(3) = {x}^(3) - {y}^(3) + 3xy(y - x) \\ \\ { \boxed{( {x}^(3) - {y}^(3) ) = {(x - y)}^(3) - 3xy(y - x)}}`

take y to be 3, then substitute:

`( {x}^(3) - 3^3) = {(x - 3)}^(3) - 9x(3 - x)`