1.

(i) a^3 - b^3; a - b.​

Answer»

Step-by-step EXPLANATION:

We know the identity a

3

−b

3

=(a−b)(a

2

+b

2

+ab)

USING the above identity, the EQUATION a

3

−b

3

−a+b can be factorised as follows:

a

3

−b

3

−a+b=(a

3

−b

3

)−(a−b)={(a−b)[(a)

2

+(b)

2

+(a×b)]}−(a−b)= [(a−b)(a

2

+b

2

+ab)]−(a−b)

=(a−b)(a

2

+b

2

+ab−1)

HENCE, a

3

−b

3

−a+b=(a−b)(a

2

+b

2

+ab−1)


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