Question

Factorise 27x3 +y3 +23-9xyz
15. Verify that
x3 +y3 +23 – 3xyz = 12 (x + y +z)[(x-y)2 + (y - 3)2 +(z – x)2]​

Answer 1

Answer

27x

3

+y

3

+z

3

−9xyz

=(3x)

3

+y

3

+z

3

−9xyz

=(3x)

3

+y

3

+z

3

−3×3x×y×z

using identity

a

3

+b

3

+c

3

−3abc=(a+b+c)(a

2

+b

2

+c

2

−ab−bc−ca)

Putting a=3x,b=y,c=z

=(3x+y+z)(9x

2

+y

2

+z

2

−3xy−yz−3zx).