Question

Factorise (a+b)^3 -a-b

Answer 1

(a+b)^3-a-bWe know the identity a

3

−b

3

=(a−b)(a

2

+b

2

+ab)

Using the above identity, the equation 1−x

3

can be factorised as follows:

a

3

−2

2

b

3

=(a)

3

−(

2

b)

3

=(a−

2

b)[(a)

2

+(

2

b)

2

+(a×

2

b)]=(a−

2

b)(a

2

+2b

2

+

2

ab)

Hence, a

3

−2

2

b

3

=(a−

2

b)(a

2

+2b

2

+

2

ab)