Réponses

2013-09-22T13:21:27+02:00
(a + b)³ = (a + b) * (a + b) * (a + b)

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

= (a² + ab + ba + b²) * (a + b)

ab=ba
(a²+2ab+b²)(a+b) 
=

= (a² * a) + (a² * b) + (2ab * a) + (2ab * b) + (b² * a) + (b² * b)

= a³ + a²b + 2a²b + 2ab² + ab² + b³

= a³ + 3a²b + 3ab² + b³

(a-b)³=a³-3a²b+3ab²-b³

=(a-b)*(a-b)*(a-b)

=[(a-b)*(a-b)]*(a-b)

=(a²-ab-ba+b²)(a-b)

=(a²-2ab+b²)(a-b)

=a³ -2 a²b + ab²-a²b+2ab² + b³

=a³-3a²b+3ab²-b³