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

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

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expand (2x-3y)^3

expand

(2 x - 3 y)^{3}

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

Solution steps

(2 x - 3 y)^{3}

Apply Perfect Cube Formula:

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

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

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

Simplify

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

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

2 \cdot (- \frac{1}{2})

(x - 7) (x + 3)

\frac{20}{5}

(x - 4) (x - 2)

16 \div 4

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