Question

If x - y = 3(z-y), then (x³ + 8y³-27z³)÷(xyz) = ​

Answer 1

-18

Explanation:

You want the value of (x³ + 8y³-27z³)÷(xyz) given that x -y = 3(z -y).

Substitution

Solving the constraint equation for x gives ...

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

Substituting this into the expression we want the value of, we have ...

`((3z-2y)^3+8y^3-27z^3)/((3z-2y)yz)\\\\\\=((3z-2y)^3+(2y-3z)((2y)^2+(2y)(3z)+(3z)^2))/(yz(3z-2y))\\\\\\=((3z-2y)^2-((3z)^2+6yz+(2y)^2))/(yz)=(-12yz-6yz)/(yz)=\boxed{-18}`

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Additional comment

We have used the factoring of the difference of cubes:

a³ -b³ = (a -b)(a² +ab +b²)

And the expansion of a binomial square:

(a -b)² = a² -2ab +b²

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