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Popular Álgebra >

desarrollar (2m^3-3n^4)^4

Solución

desarrollar

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

Solución

16 m^{12} - 96 m^{9} n^{4} + 216 m^{6} n^{8} - 216 m^{3} n^{12} + 81 n^{16}

Pasos de solución

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

Aplicar el teorema del binomio:

(a + b)^{n} = i = 0 \sum n (i n) a^{(n - i)} b^{i}

a = 2 m^{3}, b = - 3 n^{4}

= i = 0 \sum 4 (i 4) (2 m^{3})^{(4 - i)} (- 3 n^{4})^{i}

Expandir sumatorio

= \frac{4 !}{0 ! ( 4 - 0 ) !} (2 m^{3})^{4} (- 3 n^{4})^{0} + \frac{4 !}{1 ! ( 4 - 1 ) !} (2 m^{3})^{3} (- 3 n^{4})^{1} + \frac{4 !}{2 ! ( 4 - 2 ) !} (2 m^{3})^{2} (- 3 n^{4})^{2} + \frac{4 !}{3 ! ( 4 - 3 ) !} (2 m^{3})^{1} (- 3 n^{4})^{3} + \frac{4 !}{4 ! ( 4 - 4 ) !} (2 m^{3})^{0} (- 3 n^{4})^{4}

Simplificar

\frac{4 !}{0 ! ( 4 - 0 ) !} (2 m^{3})^{4} (- 3 n^{4})^{0} : 16 m^{12}

Simplificar

\frac{4 !}{1 ! ( 4 - 1 ) !} (2 m^{3})^{3} (- 3 n^{4})^{1} : - 96 m^{9} n^{4}

Simplificar

\frac{4 !}{2 ! ( 4 - 2 ) !} (2 m^{3})^{2} (- 3 n^{4})^{2} : 216 m^{6} n^{8}

Simplificar

\frac{4 !}{3 ! ( 4 - 3 ) !} (2 m^{3})^{1} (- 3 n^{4})^{3} : - 216 m^{3} n^{12}

Simplificar

\frac{4 !}{4 ! ( 4 - 4 ) !} (2 m^{3})^{0} (- 3 n^{4})^{4} : 81 n^{16}

= 16 m^{12} - 96 m^{9} n^{4} + 216 m^{6} n^{8} - 216 m^{3} n^{12} + 81 n^{16}

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