Adyamadyenantyamantyena: The First by the First and the Last by the Last

Adyamadyenantyamantyena is the corollary to Urdhva-Tiryagbyham, the third sutra of Vedic mathematics.

What follows is a brief and incomplete summary of the math shortcuts this corollary contains:

Practical Application: calculating the area of a wall in feet and inches
This is not much of a shortcut but can be useful for estimating in one's head.
Example: wall is 9'5" x 10'7"
Rewrite this as (9z + 5) x (10z + 7). z equals 12 inches. z squared equals 1 square foot
Cross-multiplying this, we get: (9z x 10z) + (5 x 10z) + (5 x 7) + (9z x 7)
This simplifies to: 90z2 + 50z + 35 + 63z
Which simplifies to: 90 square feet + 113z +35
The 113 can be divided by 12 (144/z = 12) to simplify it into square feet also, simplifying the answer to: 99 square feet + 5z + 35
This simplifies to 99 square feet + (5 x 12) + 35
The answer is 99 square feet and 95 square inches

Adyamadyenantyamantyena can be used in conjunction with Anurupyena to factor quadratic equations. If you want to learn this method, check out the resources listed below:

Vedic Mathematics by Sri Bharati Krisna Tirthaji
Mathemagics by Arthur Benjamin and Michael B. Shermer