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

2 Answers | Add Yours

justaguide's profile pic

justaguide | College Teacher | (Level 2) Distinguished Educator

Posted on

We have to prove the identity 3+(4+x)^3=x^3+12x^2+115

Starting with the left hand side

3+(4+x)^3

=> 3 + 4^3 + x^3 + 3*16*x + 3*4*x^2

=> 3 + 64 + x^3 + 48x + 12x^2

=> x^3 + 12x^2 + 48x + 67

We see that this is not equal to the right hand side.

Therefore the expression that we have is not an identity that can be proved.

giorgiana1976's profile pic

giorgiana1976 | College Teacher | (Level 3) Valedictorian

Posted on

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.

We’ve answered 318,994 questions. We can answer yours, too.

Ask a question