Question

If f(x) = x(x+1)(2x+1) , prove that f(x)-f(x-1)= 6x2​

Answer 1

Step-by-step explanation:

f(x) = x(x + 1) (2x + 1)

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

= 2x^3 + 3x^2 + x

f(x - 1) = (x - 1) ( x - 1 + 1) [2(x - 1) + 1] = x(x - 1) (2x - 1)

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

= 2x^3 - 3x^2 + x

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