Question

hibfriends
please help me do this question...

Answer 1

27x3 + y3 + z3 - 9xyz

             = (3x)3 + y3 + z3 - 3 × (3x) × y × z  

             = [3x + y + z ][(3x)2 + y2 + z2 - (3x) × y − y × z  − z(3x)] [Since  (a + b + c )(a2 + y2 + z2 - ab−bc−ca)]

             = [3x + y + z ][9x2 + y2 + z2 - 3xy − yz  − 3zx]

Answer 2

Given Equation is 27x^3 + y^3 + z^3 - 9xyz.

It can be written as,

= > (3x)^3 + (y)^3 + (z)^3 - 3(3x)(y)(z)

It is in the form of a^3 + b^3 + c^3 - 3abc = (a+b+c)(a^2 + b^2 + c^2 - ab - bc - ca)

= > (3x + y + z)((3x)^2 + (y)^2 + (z)^2 - (3x)(y) - (yz) - (z)(3x)

= > (3x + y + z)(9x^2 + y^2 + z^2 - 3xy - yz - 3xz).

Hope this helps!