Question

Hallar el resultado, utilizando la formula del
Binomio de Newton

$a) ( m + n ) {}^{4} =$
$b) \: (2x + y) { }^{5} =$
$c) \: (a {}^{2} - b {}^{2} ) {}^{6 = }$

​me ayudan por fa doy coronas

Answer 1

Respuesta:

Explicación paso a paso:

Binomio de Newton

$(a+b)^n=\sum_{k=0}^{n} \binom{n}{k} a^{n-k}b^k$

Combinatoria

$\binom{n}{k} = \frac{n!}{k!(n-k)!}$

$a) (m+n)^4$

$(m+n)^4 = \sum_{k=0}^{4} \binom{4}{k} m^{4-k}n^k$

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

$(m+n)^4 = m^{4}\binom{4}{0}+m^{3}n\binom{4}{1}+m^{2}n^2\binom{4}{2}+mn^3\binom{4}{3}+n^4\binom{4}{4}$

$(m+n)^4 = m^{4}(1)+m^{3}n(4)+m^{2}n^2(6)+mn^3(4)+n^4(1)$

$(m+n)^4 = m^{4}+4m^{3}n+6m^{2}n^2+4mn^3+n^4$