Question

(x-1)³-(x-3)(x²+3x+9)-3x(1-x)

Answer 1

( x - 1)\(^3\) - (x - 3)(x\(^2\)+ 3x + 9) - 3x( 1 - x)

= x\(^3\) + 3x\(^2\)- 3x + 1 - (x - 3)(x+3)\(^2\)- 3x + 3x\(^2\)

= x\(^3\)+ (3x\(^2\) + 3x\(^2\)) - (3x + 3x) + 1 - (x - 3)(x+3)\(^2\)

= x\(^3\)+ 6x\(^2\)- 6x + 1 + (x + 3)(x+3)\(^2\)

= x\(^3\)+ 6x\(^2\)- 6x + 1 + (x + 3)\(^3\)

= x\(^3\)+ 6x\(^2\)- 6x + 1 + x\(^3\)+ 9x\(^2\) + 27x + 27

= (x\(^3\) - x\(^3\)) + (6x\(^2\)+9x\(^2\)) - (6x - 27x) + (1 + 27)

= 15x\(^2\) + 21x + 28