Question

Factorise a-b-a
3-b3​

Answer 1

Answer:

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)

Step-by-step explanation:

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