# Formulas of abridged multiplication

From the rules of multiplication of sums and polynomials the following seven formulas of abridged multiplication can be easily received.
*
It is necessary
to know them by heart,
*
as they are used in most of problems in mathematics.

[1]
**
( a + b )
**

*² = a ² + 2ab + b ² ,*
[2]
**
( a
**
–

*b )***–**

*² = a ²*

*2ab + b*

*² ,*
[3]
**
( a + b ) ( a
**
–

*b ) = a***–**

*²*

*b*

*² ,*
[4]
**
( a + b )
**

*³*

*= a*

*³ + 3a ² b + 3ab ² + b ³ ,*
[5]
**
( a
**
–

*b )*

*³*

*= a***–**

*³*

*3a***–**

*² b + 3ab ²*

*b*

*³ ,*
[6]
**
( a + b )( a
**

**–**

*²*

*ab + b*

*² ) = a ³ + b ³ ,*
[7]
**
( a
**
–

*b )( a*

*² +*

*ab + b***–**

*² ) = a ³*

*b*

*³ .*
E x a m p l e : Calculate 99³ using the formula [5] .

S o l u t i o n : 99³ = (100 – 1)³ = 1000000 – 3 ·10000 ·1 + 3 ·100 ·1 – 1 = 970299.