What is expand (3x-3y)^3 ?

The solution to expand (3x-3y)^3 is 27x^3-81x^2y+81xy^2-27y^3

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expand (3x-3y)^3

expand

(3 x - 3 y)^{3}

27 x^{3} - 81 x^{2} y + 81 x y^{2} - 27 y^{3}

Solution steps

(3 x - 3 y)^{3}

Apply Perfect Cube Formula:

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

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

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

Simplify

(3 x)^{3} - 3 (3 x)^{2} \cdot 3 y + 3 \cdot 3 x (3 y)^{2} - (3 y)^{3} : 27 x^{3} - 81 x^{2} y + 81 x y^{2} - 27 y^{3}

= 27 x^{3} - 81 x^{2} y + 81 x y^{2} - 27 y^{3}

(2 y^{3} + 4 y^{2} + 3) + (15 y^{4} + 10 y^{3} - 3 y^{2})

93 a^{3} \cdot x^{2} \cdot y - 62 a^{2} \cdot x^{3} \cdot y^{2} - 124 a^{2} \cdot x

(- 3 a)^{3}

- 4 a (a^{- 1} \cdot b^{2})^{3}

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

What is expand (3x-3y)^3 ?
The solution to expand (3x-3y)^3 is 27x^3-81x^2y+81xy^2-27y^3