Question

Factorize a3 -8
upon b3​

Answer 1

Answer:

a³-b³ = (a-b) {a²+b²+ab}

Step-by-step explanation:

a³-8

______

b³

a³-(2)³

______

b³

(a-2) { a²+b²+ab}

________________

b³

if you want to prove this formula

a³-b³=(a-b){a²+b²+ab}

Proof of

a³ – b³ = (a – b)(a² + ab + b²)

we 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 )

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