Question

Factorise:
(a+b) cube - (a-b)
With steps please.. ​

Answer 1

Answer:

(a+b)

3

−8=(a+b−2)((a+b)

2

+2(a+b)+2

2

)

Step-by-step explanation:

Given the polynomial

(a+b)^3-8(a+b)

3

−8

we have to factorize the above polynomial.

Using identity

x^3-y^3=(x-y)(x^2+xy+y^2)x

3

−y

3

=(x−y)(x

2

+xy+y

2

)

(a+b)^3-8(a+b)

3

−8

=(a+b)^3-2^3=(a+b)

3

−2

3

Put x=a+b, y=2

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

2

+2(a+b)+2

2

)

Answer 2

Step-by-step explanation:

(a+b) ³= a³+3a²b+3ab²+b³

(a-b) ³= a³-3a²b+3a²b-b³