Alaina was asked whether the following equation is an identity: (2x + 1)2 – (x + 1)2 = 3(x + 1)2 - 1
She performed the following steps:
(2x + 1)2 – (x + 1)2
Step 1
= 4x2 + 4x +1 - 2 + 2.0 + 1
Step 2
= 3x2 + 6x + 2
Step 3
→
= 3x² + 6x +3-1
Step
= 3(x2 + 2x + 1) - 1
Step 5
3(x + 1)2 – 1
For this reason, Alaina stated that the equation is a true identity.
Is Alaina correct? If not, in which step did she make a mistake?