Answer:
YES
Step-by-step explanation:
The equation, [tex] 3(x + 1)2 = (3x + 3)2 [/tex], 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:
[tex] 3(x + 1)2 = (3x + 3)2 [/tex]
[tex] 3(1 + 1)2 = (3(1) + 3)2 [/tex]
[tex] 3(2)2 = (3 + 3)2 [/tex]
[tex] 12 = 12 [/tex] (TRUE)
✍️Substituting x = 2 into the equation:
[tex] 3(x + 1)2 = (3x + 3)2 [/tex]
[tex] 3(2 + 1)2 = (3(2) + 3)2 [/tex]
[tex] 3(3)2 = (6 + 3)2 [/tex]
[tex] 18 = 18 [/tex] (TRUE)
✍️Substituting x = 3 into the equation:
[tex] 3(x + 1)2 = (3x + 3)2 [/tex]
[tex] 3(3 + 1)2 = (3(3) + 3)2 [/tex]
[tex] 3(4)2 = (9 + 3)2 [/tex]
[tex] 24 = 24 [/tex] (TRUE)
Therefore, we can conclude that the equation, [tex] 3(x + 1)2 = (3x + 3)2 [/tex], is an identity.
