Question

prove that a³-b³=(a-b)(a²+ab+b²)​

Answer 1

Answer:

Step-by-step explanation:

(a-b)³

= (a-b)(a-b)(a-b)

=(a-b)(a²-ab-ab+b²)

=(a-b)(a²-2ab+b²)

= a³-2a²b+ab²-a²b+2ab²-b³

= a³- b³ - 3a²b + 3 ab²

= a³- b³ - 3ab(a-b)

That is

a³- b³ - 3ab(a-b) = (a-b)³

Thus,

a³- b³ = (a-b)³+ 3ab(a-b)

Again,

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)

So You can write a³- b³ = (a-b)³+ 3ab(a-b)

and also, a³- b³ =(a-b)(a²+ab+b²