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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  =  a²  + 2ab + b² ,

                              [2]       ( a b )²  =  a²  2ab + b² ,

                              [3]       ( a + b ) ( a b ) = a²    b²,

                              [4]       ( a + b )³  =  a³  + 3a² b + 3ab²  + b³ ,

                              [5]       ( a b )³  =  a ³  3a² b + 3ab²  b³ ,

                              [6]       ( a + b )( a²  ab + b² ) =  a³ + b³ ,

                              [7]       ( a b )( a ²  + ab + b² ) =  a³ b³ .

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.

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