Question

f(x)=x(x+1)(2x+1) then f(x)-f(x-1)= ?

Answer 1

The answer is given below :

Given,

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

Now, to find f(x - 1), just replace x by (x - 1).

So,

f(x - 1)

= (x - 1)(x - 1 + 1){2(x - 1) + 1}

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

= (x - 1)(x)(2x - 1)

= x(x - 1)(2x - 1)

Now,

f(x) - f(x - 1)

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

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

= x[(2x² + x + 2x + 1) - (2x² - x - 2x + 1)]

= x[2x² + 3x + 1 - 2x² + 3x - 1]

= x[6x]

= 6x² [Answer]

Thank you for your question.