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

The solution to expand (3xy-2y)^3 is 27x^3y^3-54y^3x^2+36xy^3-8y^3

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expand (3xy-2y)^3

expand

(3 x y - 2 y)^{3}

27 x^{3} y^{3} - 54 y^{3} x^{2} + 36 x y^{3} - 8 y^{3}

Solution steps

(3 x y - 2 y)^{3}

Apply Perfect Cube Formula:

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

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

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

Simplify

(3 x y)^{3} - 3 (3 x y)^{2} \cdot 2 y + 3 \cdot 3 x y (2 y)^{2} - (2 y)^{3} : 27 x^{3} y^{3} - 54 y^{3} x^{2} + 36 x y^{3} - 8 y^{3}

= 27 x^{3} y^{3} - 54 y^{3} x^{2} + 36 x y^{3} - 8 y^{3}

\frac{3}{( x ^{2} + 3 x )} - \frac{1}{x} - \frac{6}{( x ^{2} - 9 )}

50 a^{2} + 75 a^{2} \cdot b

x^{4} y - x y^{4}

2 x^{9} + x^{9} + (- 2)

2 x^{3} - 2 x^{2} - 8 x

What is expand (3xy-2y)^3 ?
The solution to expand (3xy-2y)^3 is 27x^3y^3-54y^3x^2+36xy^3-8y^3