Factorize the following: 9x2 + 6x + 1 – 25y2

Sure, let's factorize the given expression step by step:

The given expression is 9x^2 + 6x + 1 – 25y^2

First, we can see that the expression 9x^2 + 6x + 1 is a perfect square trinomial. It can be written as (3x+1)^2.

So, the expression becomes (3x+1)^2 - 25y^2

Now, we can see that the expression is a difference of squares, which can be factored as (a+b)(a-b).

So, the factorized form of the expression is ((3x+1) + 5y)((3x+1) - 5y).

So, the factorized form of 9x^2 + 6x + 1 – 25y^2 is ((3x+1) + 5y)((3x+1) - 5y).