What is expand (9x-3y)^3 ?

The solution to expand (9x-3y)^3 is 729x^3-729x^2y+243xy^2-27y^3

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expand (9x-3y)^3

expand

(9 x - 3 y)^{3}

729 x^{3} - 729 x^{2} y + 243 x y^{2} - 27 y^{3}

Solution steps

(9 x - 3 y)^{3}

Apply Perfect Cube Formula:

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

(9 x - 3 y)^{3} = (9 x)^{3} - 3 (9 x)^{2} \cdot 3 y + 3 \cdot 9 x (3 y)^{2} - (3 y)^{3}

= (9 x)^{3} - 3 (9 x)^{2} \cdot 3 y + 3 \cdot 9 x (3 y)^{2} - (3 y)^{3}

Simplify

(9 x)^{3} - 3 (9 x)^{2} \cdot 3 y + 3 \cdot 9 x (3 y)^{2} - (3 y)^{3} : 729 x^{3} - 729 x^{2} y + 243 x y^{2} - 27 y^{3}

= 729 x^{3} - 729 x^{2} y + 243 x y^{2} - 27 y^{3}

3 q^{2} + q - q^{2}

- 3 - (- 10)

(x + 3) (x - 3) (x)

10 - (- 1)

x^{5} + x^{3} + x^{2} + 1

What is expand (9x-3y)^3 ?
The solution to expand (9x-3y)^3 is 729x^3-729x^2y+243xy^2-27y^3