Question

Subtract a3 - 3a2 from b3 - 3b2.​

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 )

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 )

Step-by-step explanation:

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