Vedic Mathematics/Sutras/Urdhva-Tiryagbyham

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Multiplication of a 2 figure integer $$ab$$ by another 2 figures integer $$cd$$ :

$$\begin{matrix}a & & b\\ \vert& \times & \vert\\c & & d\\a*c & ad+bc & b*d\end{matrix} $$ For Example, 12 × 23 = ( 1×2 ) | ( 1×3 + 2×2 ) | ( 3×2 ) = 276

or in base 10:

$$(10 a+b) (10c +d) = 100 (a*c) + 10(ad+cb) + (b*d) $$

of course, the cases where $$(ad+cb)>10$$ or $$b+d>10$$ are to be considered.

Let us take the above example in another way. While multiplying 2 digit numbers with each other,
 * Step 1: the product of the last digits in both numbers becomes the last digit of the result. Therefore the last digit of the result is 2*3=6
 * Step 2: the first digit of the first number is multiplied with the second digit of the second number i.e.1*3=3. Now,the last digit of the first number is multiplied with the first digit of the second number i.e.
 * 2*2=4. Both these numbers are now added
 * 3+4=7. This becomes the second digit of the result
 * Step 3: The first digit of the product is obtained by multiplying the first digits of both numbers, i.e. 1*2=2

Our final answer is 276.