Question

Prove the polynomial identity.

Answer 1

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.