Question

a3 + 3a.2 b + 3a6² +6²-8​

Answer 1

Answer:

We solve the given expression a

3

+3a

2

b+3ab

2

+b

3

−8 as shown below:

a

3

+3a

2

b+3ab

2

+b

3

−8

=(a+b)

3

−(2)

3

(∵(x+y)

3

=x

3

+y

3

+3x

2

y+3xy

2

)

=(a+b−2)[(a+b)

2

+2

2

+2(a+b)](∵x

3

−y

3

=(x−y)(x

2

+y

2

+xy))

=(a+b−2)(a

2

+b

2

+2ab+4+2a+2b)(∵(x+y)

2

=x

2

+y

2

+xy)

Hence, a

3

+3a

2

b+3ab

2

+b

3

−8=(a+b−2)(a

2

+b

2

+2ab+4+2a+2b)

Answer 2

REFER TO THE ATTACHMENT.