State that identity is true: 3+(4+x)^3=x^3+12x^2+115

We'll manage the left side and we'll expand the
cube:

(4+x)^3 = 4^3 + x^3 +
3*4*x(4+x)

(4+x)^3 = 64 + x^3 +
12*x(4+x)

We'll remove the brackets from the
right:

(4+x)^3 = 64 + x^3 + 12*x^2 +
48x

We'll add 3 both
sides:

(4+x)^3 + 3 = 64 + x^3 + 12*x^2 + 48x +
3

We'll combine like
terms:

(4+x)^3 + 3 = x^3 + 12*x^2 + 48x +
67

We notice that the right side of the identity to be
demonstrated does not have the term in x, so, the both sides expressions are  not
equivalent.

The given expression does not
represent an identity.