Question

Find the following product:

(4x − 3y + 2z) (16x² + 9y² + 4z² + 12xy + 6yz − 8zx)

Answer 1

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

Given (4x − 3y + 2z) (16x² + 9y² + 4z² + 12xy + 6yz − 8zx)

We shall use the identity 

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

` = (4x)^3 + (3y)^3 + (2z)^3  -3 (4x)(3y)(2z)`

` = (4x) xx (4x) xx (4x) +(-3y) xx (-3y) xx (-3y) + (2z) xx (2z) xx (2z)  -3 (4x) (-3y)(2z)`

` = 64x^3 - 27y^3 + 8z^3 + 72 xyz`

Hence the product of (4x − 3y + 2z) (16x² + 9y² + 4z² + 12xy + 6yz − 8zx) is `64x^2 - 27y^3 + 8z^3 + 72xyz`