# Multiplication - Shortcuts

Product of two numbers =Product of their H.C.F. and L.C.M.

## 1. Multiplication By Distributive Law :

- a x (b + c) = a x b + a x c
- ax(b-c) = a x b-a x c.

## 2. Multiplication of a Number By 5n

: Put n zeros to the right of the multiplicand and
divide the number so formed by 2^{n}

## BASIC FORMULAE

- (a + b)2 = a2 + b2 + 2ab
- (a - b)2 = a2 + b2 - 2ab
- (a + b)2 - (a - b)2 = 4ab
- (a + b)2 + (a - b)2 = 2 (a2 + b2)
- (a2 - b2) = (a + b) (a - b)
- (a + b + c)2 = a2 + b2 + c2 + 2 (ab + bc + ca)
- (a3 + b3) = (a +b) (a2 - ab + b2)
- (a3 - b3) = (a - b) (a2 + ab + b2)
- (a3 + b3 + c3 -3abc) = (a + b + c) (a2 + b2 + c2 - ab - bc - ca)
- If a + b + c = 0, then a3 + b3 + c3 = 3abc.