Question

factorization
a3+b3+a+b​

Answer 1

Given a^3 +b^3 +a + b

a3 + b3 = (a + b) (a^2 - ab + b^2 ).

= (a + b) (a^2 - ab + b^2 )+(a+b)

=(a+b)(a^2 + ab +b^2 +1).

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Answer 2

Step-by-step explanation:

Factorise: a3 - b3 - a + b

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)