Question

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

Answer 1

Answer:

YES

Step-by-step 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.