Question

Is 3(x + 1)2 = (3x + 3)2 an identity? Explain and show your reasoning.

Answer 1

YES

Explanation:

The equation,
`3(x + 1)2 = (3x + 3)2`, would be an identity if the equation remains true regardless of the value of x we choose to plug in into the equation.

Let's find out if we would always get a true statement using different value of x.

✍️Substituting x = 1 into the equation:

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

`3(1 + 1)2 = (3(1) + 3)2`

`3(2)2 = (3 + 3)2`

`12 = 12` (TRUE)

✍️Substituting x = 2 into the equation:

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

`3(2 + 1)2 = (3(2) + 3)2`

`3(3)2 = (6 + 3)2`

`18 = 18` (TRUE)

✍️Substituting x = 3 into the equation:

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

`3(3 + 1)2 = (3(3) + 3)2`

`3(4)2 = (9 + 3)2`

`24 = 24` (TRUE)

Therefore, we can conclude that the equation,
`3(x + 1)2 = (3x + 3)2`, is an identity.