Vedic Maths : ekanyunena purvena Again
ekanyunena purvena
'One less than the previous' or 'One less than the one before'
एकन्यूनेन पूर्वेन
Now we will cover another special case of multiplying with ( x - 1)
A = px + a and B = x - 1
So A * B = (px + a) * ( x - 1)
= p * ( x ^ 2 ) - px + ax - a
= p * ( x ^ 2 ) - px + ax - a + x - x
= x ( px - p + a - 1 ) + ( x - a )
= x ( px + a - p - 1 ) + ( x - a )
As we know A = px + a
A * B = x ( A - p - 1) + ( x - a )
Also,
A * B = x * [ A - ( p + 1 ) ] + ( x - a )
Here are examples
|
B = x - 1 |
p |
a |
n |
A – p – 1 |
x - a |
|
|
11 |
1 |
1 |
11 – 1 – 1 = 9 |
9 |
||
|
12 |
9 |
1 |
2 |
12 – 1 – 1 = 10 |
8 |
|
|
13 |
9 |
1 |
3 |
1 |
13 – 1 – 1 = 11 |
7 |
|
14 |
9 |
1 |
4 |
1 |
14 – 1 – 1 = 12 |
6 |
|
15 |
9 |
1 |
5 |
1 |
15 – 1 – 1 = 13 |
5 |
|
16 |
9 |
1 |
6 |
1 |
16 – 1 – 1 = 14 |
4 |
|
17 |
9 |
1 |
7 |
1 |
17 – 1 – 1 = 15 |
3 |
|
18 |
9 |
1 |
8 |
1 |
18 – 1 – 1 = 16 |
2 |
|
19 |
9 |
1 |
9 |
1 |
19
– 1 – 1 = 17 |
1 |
|
20 |
9 |
2 |
0 |
1 |
20 – 2 – 1
= 17 |
10 |
|
21 |
9 |
2 |
1 |
1 |
21
– 2 – 1 = 18 |
9 |
|
22 |
9 |
2 |
2 |
1 |
22 – 2 – 1
= 19 |
8 |
|
23 |
9 |
2 |
3 |
1 |
23
– 2 – 1 = 20 |
7 |
|
24 |
9 |
2 |
4 |
1 |
24 – 2 – 1
= 21 |
6 |
|
25 |
9 |
2 |
5 |
1 |
25
– 2 – 1 = 22 |
5 |
|
26 |
9 |
2 |
6 |
1 |
26 – 2 – 1
= 23 |
4 |
|
27 |
9 |
2 |
7 |
1 |
27
– 2 – 1 = 24 |
3 |
|
28 |
9 |
2 |
8 |
1 |
28 – 2 – 1
= 25 |
2 |
|
29 |
9 |
2 |
9 |
1 |
29
– 2 – 1 = 26 |
1 |
|
30 |
9 |
3 |
0 |
1 |
30 – 3 – 1
= 26 |
10 |
|
37 |
9 |
3 |
7 |
1 |
37
– 3 – 1 = 33 |
3 |
|
46 |
9 |
4 |
6 |
1 |
46 – 4 – 1
= 41 |
4 |
|
55 |
9 |
5 |
5 |
1 |
55
– 5 – 1 = 49 |
5 |
|
64 |
9 |
6 |
4 |
1 |
64 – 6 – 1
= 57 |
6 |
|
73 |
9 |
7 |
3 |
1 |
73
– 7 – 1 = 65 |
3 |
|
82 |
9 |
8 |
2 |
1 |
82 – 8 – 1
= 73 |
2 |
|
91 |
9 |
9 |
1 |
1 |
91
– 9 – 1 = 81 |
1 |
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