Toán Lớp 8: Chứng minh:
$a^{3}$+ $b^{3}$=(a+b)$^{3}$-3ab(a+b)
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Toán Lớp 8: Chứng minh:
$a^{3}$+ $b^{3}$=(a+b)$^{3}$-3ab(a+b)
Comments ( 2 )
(a+b)³-3ab(a+b)
= a³ + 3.a².b + 3 .a.b² + b³ -3a²b – 3ab²
= a³ + 3a²b + 3ab² + b³ – 3a²b – 3ab²
= a³ + (3a²b- 3a²b) + (3ab²- 3ab² ) + b³
=a³ + b³
Vậy a³ + b³ = (a+b)³-3ab(a+b) (đpcm)