Factoring a quadratic by diamond method

The video tutorial demonstrates how to factor the quadratic expression 64X^2 + 16X + 1. It begins by identifying the expression as a perfect square trinomial, where the product of the coefficients a and c is 64. The tutorial explains that the numbers 8 and 8 multiply to give 64 and add to give 16, confirming the trinomial is a perfect square. The expression is then rewritten as (8X + 1)(8X + 1), and the instructor verifies the factoring by checking each term's multiplication and addition results.

What is the correct factored form of the expression 4X^2 + 16X + 1?

How can you verify that your factored expression is correct?