Verify the identity

{a}^{3} + {b}^{3} = ( {a}^{2} – ab \: + {b}^{2} )a3+b3=(a2−ab+b2)

Please answer in steps

1 thought on “Verify the identity<br /><br />{a}^{3} + {b}^{3} = ( {a}^{2} – ab \: + {b}^{2} )a3+b3=(a2−ab+b2)<br /><br />Please answer in steps”

1. Answer:

   Proof of a³ + b³ = (a + b)(a² – ab + b²)

   you know that,

   (a + b)³ = a³ + 3ab(a + b) + b³

   then

   a³ + b³ = (a + b)³ – 3ab(a + b)

   = (a + b)[(a + b)² – 3ab]

   = (a + b)(a² + 2ab + b² – 3ab)

   = (a + b)(a² – ab + b² )

   Reply