Question

Verify the identity

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

Please answer in steps please​

Answer 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 )