I just hand-derived it both ways to make a comparison, the standard way was from memory. So. The standard way to complete the square uses a trick to rearrange

I just hand-derived it both ways to make a comparison, the standard way was from memory. So. The standard way to complete the square uses a trick to rearrange the equation so that one can use the formula (a+b)^2 = a^2 + 2ab + b^2. This uses a different trick to rearrange the equation to make use of (a+b)(a-b) = a^2 - b^2. Frankly, I don’t see how this is any easier. If anything, I think it’s harder to do from memory because you need to introduce a new variable in a very specific way to make the simplification work. The standard way feels a lot more systematic.