What is expand (6mn^2-4n)^3 ?

The solution to expand (6mn^2-4n)^3 is 216m^3n^6-432n^5m^2+288mn^4-64n^3

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expand (6mn^2-4n)^3

expand

(6 m n^{2} - 4 n)^{3}

216 m^{3} n^{6} - 432 n^{5} m^{2} + 288 m n^{4} - 64 n^{3}

Solution steps

(6 m n^{2} - 4 n)^{3}

Apply Perfect Cube Formula:

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

(6 m n^{2} - 4 n)^{3} = (6 m n^{2})^{3} - 3 (6 m n^{2})^{2} \cdot 4 n + 3 \cdot 6 m n^{2} (4 n)^{2} - (4 n)^{3}

= (6 m n^{2})^{3} - 3 (6 m n^{2})^{2} \cdot 4 n + 3 \cdot 6 m n^{2} (4 n)^{2} - (4 n)^{3}

Simplify

(6 m n^{2})^{3} - 3 (6 m n^{2})^{2} \cdot 4 n + 3 \cdot 6 m n^{2} (4 n)^{2} - (4 n)^{3} : 216 m^{3} n^{6} - 432 n^{5} m^{2} + 288 m n^{4} - 64 n^{3}

= 216 m^{3} n^{6} - 432 n^{5} m^{2} + 288 m n^{4} - 64 n^{3}

- \frac{65}{121}

20 \cdot 63

\frac{5}{2} \div 3

- 6 j - (- 4) + 2 j - 1

17 g - 2 g

What is expand (6mn^2-4n)^3 ?
The solution to expand (6mn^2-4n)^3 is 216m^3n^6-432n^5m^2+288mn^4-64n^3