What is expand (2z-3w)^3 ?

The solution to expand (2z-3w)^3 is 8z^3-36z^2w+54zw^2-27w^3

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expand (2z-3w)^3

expand

(2 z - 3 w)^{3}

8 z^{3} - 36 z^{2} w + 54 z w^{2} - 27 w^{3}

Solution steps

(2 z - 3 w)^{3}

Apply Perfect Cube Formula:

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

(2 z - 3 w)^{3} = (2 z)^{3} - 3 (2 z)^{2} \cdot 3 w + 3 \cdot 2 z (3 w)^{2} - (3 w)^{3}

= (2 z)^{3} - 3 (2 z)^{2} \cdot 3 w + 3 \cdot 2 z (3 w)^{2} - (3 w)^{3}

Simplify

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

= 8 z^{3} - 36 z^{2} w + 54 z w^{2} - 27 w^{3}

\frac{( 6 x ^{3} - 22 x ^{2} + 2 x + 56 )}{( 6 x + 8 )}

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What is expand (2z-3w)^3 ?
The solution to expand (2z-3w)^3 is 8z^3-36z^2w+54zw^2-27w^3