What is expand (3m-2n^2)^3 ?

The solution to expand (3m-2n^2)^3 is 27m^3-54m^2n^2+36mn^4-8n^6

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expand (3m-2n^2)^3

expand

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

27 m^{3} - 54 m^{2} n^{2} + 36 m n^{4} - 8 n^{6}

Solution steps

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

Apply Perfect Cube Formula:

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

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

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

Simplify

(3 m)^{3} - 3 (3 m)^{2} \cdot 2 n^{2} + 3 \cdot 3 m (2 n^{2})^{2} - (2 n^{2})^{3} : 27 m^{3} - 54 m^{2} n^{2} + 36 m n^{4} - 8 n^{6}

= 27 m^{3} - 54 m^{2} n^{2} + 36 m n^{4} - 8 n^{6}

2 cos (x) \cdot sin (x)

(\frac{1 + i}{1 - i})^{8}

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

\frac{46}{7}

6 m^{2} - 25 m - 9

What is expand (3m-2n^2)^3 ?
The solution to expand (3m-2n^2)^3 is 27m^3-54m^2n^2+36mn^4-8n^6