Let us simplify using formula:-
`(x+1) (x^2 - x + 1) + (2x - 1) (4x^2 + 2x + 1) - (x-1)(x^2 + x + 1)`

If g(x) = 1/x^2 , show that , g(x) - g(x + 1) = (2x + 1)/(x^2 (x + 1)^2) .

Simplify the following: 3x^2 + x (x+2) -3x (2x +1)

Simplify : (x + sqrt(x^(2) - 1))/(x - sqrt(x^(2) -1)) + (x - sqrt(x^(2) -1))/(x + sqrt(x^(2) -1)) If the result of the simplification is equal to 14, then find the value of x

Use suitable identities to find the following products (i) (x +5) (x +2) (ii) (x-5) (x-5) (iii) (3x +3) (3x -2) (iv) (x ^(2) + (1)/( x ^(2)) )(x ^(2) - (1)/( x ^(2))) (v) (1+x) (1+x)

int ((x^2 -1)dx)/((x^4 + 3x^2 + 1) tan^-1((x^2 + 1)/x)) = k logabs(tan^-1((x^2 +1)/x)) + c

Let us factorise the following. x^4 + x^2 + 1

tan ^(-1) ""(x-1)/(x-2) + tan ^(-1) ""(x+1)/(x+2)=(pi)/(4)

Using formula, let's solve each of the following problems- If 6x^2 - 1 = 4x , let's show (36x^2 + frac(1)(x^2)) = 28

Use formula lim_(x->0)(a^x-1)/x=log(a) to find lim_(x->0)(2^x-1)/((1+x)^(1/2)-1)