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 5n : Put 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
16
VII. 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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