Question

a3 - b3 in algebraic identity

Answer 1

Heya friend....
Rajdeep here!!

a³ - b³ = (a – b) (a² + ab + b²)

Thanks!!

Answer 2

Answer:

a³-b³ = (a-b)(a²+ab+b²)

Or

a³-b³ = (a-b)³+3ab(a-b)

Explanation:

we know the algebraic identity:

i )(a-b)³ = a³-3a²b+3ab²-b³

= a³-b³-3a²b+3ab²

= a³-b³-3ab(a-b)

=> (a-b)³+3ab(a-b)=a³-b³

Therefore,

$\boxed {a^{3}-b^{3}=(a-b)^{3}+3ab(a-b)}$---(1)

Or

ii ) a³-b³ = (a-b)³+3ab(a-b)/* from (1)*/

Take (a-b) common, we get

= (a-b)[(a-b)²+3ab]

= (a-b)(a²-2ab+b²+3ab)

/* By algebraic identity :

(a-b)² = a²-2ab+b² */

= (a-b)(a²+ab+b²) ---(2)

Therefore,

a³-b³

= (a-b)³+3ab(a-b)

Or

= (a-b)(a²+ab+b²)

•••••