Question

(x + 2y)⁶ me ayudan por favor, es tarea para hoy ​

Answer 1

Respuesta:

$\left(x\:+\:2y\right)^6$

Teorema del Binomio

$\left(a+b\right)^n=\sum _{i=0}^n\binom{n}{i}a^{\left(n-i\right)}b^i$

$\sum _{i=0}^6\binom{6}{i}x^{\left(6-i\right)}\left(2y\right)^i$

$\frac{6!}{0!\left(6-0\right)!}x^6\left(2y\right)^0=x^6$

$\frac{6!}{1!\left(6-1\right)!}x^5\left(2y\right)^1=12x^5y$

$\frac{6!}{2!\left(6-2\right)!}x^4\left(2y\right)^2=60x^4y^2$

$\frac{6!}{3!\left(6-3\right)!}x^3\left(2y\right)^3=160x^3y^3$

$\frac{6!}{4!\left(6-4\right)!}x^2\left(2y\right)^4=240x^2y^4$

$\frac{6!}{5!\left(6-5\right)!}x^{1} (2y)^{5} =192xy^5$

$\frac{6!}{6!\left(6-6\right)!}x^{0} (2y)^{6} =64y^6$

$x^6+12x^5y+60x^4y^2+160x^3y^3+240x^2y^4+192xy^5+64y^6$

Saludos...