Thursday, 22 December 2011

MULTIPLICATION BY SHORT CUT METHODS

1.  Multiplication By Distributive Law :
(i) a x (b + c) = a x b + a x c    (ii) ax(b-c) = a x b-a x c.
Ex.   (i) 567958 x 99999 = 567958 x (100000 - 1)
= 567958 x 100000 - 567958 x 1 = (56795800000 - 567958) = 56795232042.
(ii) 978 x 184 + 978 x 816 = 978 x (184 + 816) = 978 x 1000 = 978000.
2.  Multiplication of a Number By 5nPut n zeros to the right of the multiplicand and divide the number so formed by 2n
Ex. 975436 x 625 = 975436 x 54= 9754360000 =   609647600

BASIC FORMULAE
1. (a + b)2 = a2 + b2 + 2ab                     
2. (a - b)2 = a2 + b2 - 2ab
3. (a + b)2 - (a - b)2 = 4ab                       
4. (a + b)2 + (a - b)2 = 2 (a2 + b2)
5.  (a2 - b2) = (a + b) (a - b)
6.  (a + b + c)2 = a2 + b2 + c2 + 2 (ab + bc + ca)
7.  (a3 + b3) = (a +b) (a2 - ab + b2)        
8. (a3 - b3) = (a - b) (a2 + ab + b2)
9. (a3 + b3 + c3 -3abc) = (a + b + c) (a2 + b2 + c2 - ab - bc - ca)
10. If a + b + c = 0, then a3 + b3 + c3 = 3abc.


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