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

A = px + a

B = x - 1

p

a

n

A – p – 1

x - a

11

9

1

1

1

11 – 1 – 1 = 9

9

12

9

1

2

1

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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