Question

Chun was asked whether the following equation is an identity. He performed the following stepsStep 1 3(2x-1)²+27= 3 (2x-1) (2x-1)+27Step 2 = (6x-3) (6x-3)+27Step 3 = 36x²-18x-18x+9+27Step 4 = 36x²-36x+36For this reason, Chun stated that the equation is a true identity. Is Chun correct if not in which step did he make a mistake A) Chun is correctB) Chun is incorrect. He made a mistake in step 2C) Chun is incorrect. He made a mistake in step 3D) Chun is incorrect. He made a mistake in step 4

Answer 1

Chun is incorrect. He made a mistake in step 2

Let's look at the term 3(2x-1)^2

Once we factor, we have

`\begin{gathered} 3\cdot(2x-1)^2=3\cdot(2x-1)\cdot(2x-1) \\ =(6x-3)\cdot(2x-1) \end{gathered}`

He made a mistake solving the product in step 2