What is expand (3m^4-4m^3n)^3 ?

The solution to expand (3m^4-4m^3n)^3 is 27m^{12}-108m^{11}n+144m^{10}n^2-64m^9n^3

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expand (3m^4-4m^3n)^3

expand

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

27 m^{12} - 108 m^{11} n + 144 m^{10} n^{2} - 64 m^{9} n^{3}

Solution steps

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

Apply Perfect Cube Formula:

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

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

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

Simplify

(3 m^{4})^{3} - 3 (3 m^{4})^{2} \cdot 4 m^{3} n + 3 \cdot 3 m^{4} (4 m^{3} n)^{2} - (4 m^{3} n)^{3} : 27 m^{12} - 108 m^{11} n + 144 m^{10} n^{2} - 64 m^{9} n^{3}

= 27 m^{12} - 108 m^{11} n + 144 m^{10} n^{2} - 64 m^{9} n^{3}

218 \cdot 76

\frac{3}{10} \cdot \frac{5}{6}

\frac{x ^{2} y ^{- 3}}{x ^{3} y ^{3}}

- \frac{3}{2} \cdot 1

(3 x - a) (a + x)

What is expand (3m^4-4m^3n)^3 ?
The solution to expand (3m^4-4m^3n)^3 is 27m^{12}-108m^{11}n+144m^{10}n^2-64m^9n^3