Question

Find the following product:

(3x + 2y + 2z) (9x² + 4y² + 4z² − 6xy − 4yz − 6zx)

Answer 1

In the given problem, we have to find Product of equations

Given  (3x + 2y + 2z) (9x² + 4y² + 4z² − 6xy − 4yz − 6zx)

We shall use the identity 

`x^3 + y^3 + z^3 - 3xyz = (x+y+z) (x^2 + y^2 + z^2 - xy - yz - zx)`

` = (3x)^3 + (2y)^3 + (2z)^3 - 3 (3x)(2y)(2z)`

` =(3x) xx (3x) xx (3x) + (2y) xx(2y) xx(2y)  + (2z) xx(2z) xx(2z)-3(3x)(2y)(2z) `

` = 27x^3 + 8y^3 + 8z^3 - 36xyz`

Hence the product of   (3x + 2y + 2z) (9x² + 4y² + 4z² − 6xy − 4yz − 6zx)is  `27x^3 + 8y^3 + 8z^3 - 36xyz`