It’s a shame we only have a like button, because this post is 5 out of 5 stars!
The only way this could be better (five-and-a-half stars) is if you’d have called if squares with binomial formulas. It’s pretty clear that you are using the first and second formula when adding and subtracting, but even the numbers ending in 5 are done with the third:
For those interested, the nice thing here is how this is done in a mutually exclusive and collectively exhaustive fashion. If you are not into Vedic math and creatively picking the algorithm that you feel best suited… go with this method:
Blocks of 10
As described, use your knowledge of single digit squares and add two zeros
Split them in half
Use your knowledge of single digit multiplication tables for the left-hand-side and put 25 on the right
Up and down
Worst case scenario is now stepping over 4 unknowns to get to the next known: 20 ? ? ? ? 25 ? ? ? ? 30, etc. However you can cut that again in half by seeing it as either 2 up or 2 down.
One after the other
The first formula basically becomes the second formula if you plug in a negative number, so think of it this way rather than subtracting a positiv number. So again logically cut in half, there is only 1 up/down or 2 up/down now.
Conclusion
The first two steps come from knowledge you already have. The next two is just looking at the problem from the right angle. Finally, if you do the double-double thinking
it really just comes down to doubling numbers and adding 1 or 4. The entire setup is very elegant!
This one should be way up in the Mental Math category