What is expand (xy-2yz)^3 ?

The solution to expand (xy-2yz)^3 is x^3y^3-6y^3x^2z+12xy^3z^2-8y^3z^3

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expand (xy-2yz)^3

expand

(x y - 2 yz)^{3}

x^{3} y^{3} - 6 y^{3} x^{2} z + 12 x y^{3} z^{2} - 8 y^{3} z^{3}

Solution steps

(x y - 2 yz)^{3}

Apply Perfect Cube Formula:

(a - b)^{3} = a^{3} - 3 a^{2} b + 3 a b^{2} - b^{3}

(x y - 2 yz)^{3} = (x y)^{3} - 3 (x y)^{2} \cdot 2 yz + 3 x y (2 yz)^{2} - (2 yz)^{3}

= (x y)^{3} - 3 (x y)^{2} \cdot 2 yz + 3 x y (2 yz)^{2} - (2 yz)^{3}

Simplify

(x y)^{3} - 3 (x y)^{2} \cdot 2 yz + 3 x y (2 yz)^{2} - (2 yz)^{3} : x^{3} y^{3} - 6 y^{3} x^{2} z + 12 x y^{3} z^{2} - 8 y^{3} z^{3}

= x^{3} y^{3} - 6 y^{3} x^{2} z + 12 x y^{3} z^{2} - 8 y^{3} z^{3}

x^{4} + 2 x^{2} y^{2} + 9 y^{4}

\frac{200}{60}

227 + 243

(x^{2} + 2) (x - 1)

x^{- 4} \cdot x^{3}

What is expand (xy-2yz)^3 ?
The solution to expand (xy-2yz)^3 is x^3y^3-6y^3x^2z+12xy^3z^2-8y^3z^3