Question

Prove the polynomial identity.

Answer 1

Step-by-step explanation:

Since we have given that

`(2x+1)^2-2(2x+1)`

Now, we have to prove it as

`(2x+1)(2x-1)`

Now, start the iterations:

`(2x+1)^2-2(2x+1)\\\\=4x^2+1+4x-4x-2\\\\=4x^2+1-2\\\\=4x^2-1\\\\=(2x)^2-1\\\\=(2x+1)(2x-1)`

So, first blank will be filled with

`4x^2+4x+1`

Second blank will be filled with

`4x^2-1`

Hence proved.