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Popular Álgebra >

desarrollar (2x+5y)^6

Solución

desarrollar

(2 x + 5 y)^{6}

Solución

64 x^{6} + 960 x^{5} y + 6000 x^{4} y^{2} + 20000 x^{3} y^{3} + 37500 x^{2} y^{4} + 37500 x y^{5} + 15625 y^{6}

Pasos de solución

(2 x + 5 y)^{6}

Aplicar el teorema del binomio:

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

a = 2 x, b = 5 y

= i = 0 \sum 6 (i 6) (2 x)^{(6 - i)} (5 y)^{i}

Expandir sumatorio

= \frac{6 !}{0 ! ( 6 - 0 ) !} (2 x)^{6} (5 y)^{0} + \frac{6 !}{1 ! ( 6 - 1 ) !} (2 x)^{5} (5 y)^{1} + \frac{6 !}{2 ! ( 6 - 2 ) !} (2 x)^{4} (5 y)^{2} + \frac{6 !}{3 ! ( 6 - 3 ) !} (2 x)^{3} (5 y)^{3} + \frac{6 !}{4 ! ( 6 - 4 ) !} (2 x)^{2} (5 y)^{4} + \frac{6 !}{5 ! ( 6 - 5 ) !} (2 x)^{1} (5 y)^{5} + \frac{6 !}{6 ! ( 6 - 6 ) !} (2 x)^{0} (5 y)^{6}

Simplificar

\frac{6 !}{0 ! ( 6 - 0 ) !} (2 x)^{6} (5 y)^{0} : 64 x^{6}

Simplificar

\frac{6 !}{1 ! ( 6 - 1 ) !} (2 x)^{5} (5 y)^{1} : 960 x^{5} y

Simplificar

\frac{6 !}{2 ! ( 6 - 2 ) !} (2 x)^{4} (5 y)^{2} : 6000 x^{4} y^{2}

Simplificar

\frac{6 !}{3 ! ( 6 - 3 ) !} (2 x)^{3} (5 y)^{3} : 20000 x^{3} y^{3}

Simplificar

\frac{6 !}{4 ! ( 6 - 4 ) !} (2 x)^{2} (5 y)^{4} : 37500 x^{2} y^{4}

Simplificar

\frac{6 !}{5 ! ( 6 - 5 ) !} (2 x)^{1} (5 y)^{5} : 37500 x y^{5}

Simplificar

\frac{6 !}{6 ! ( 6 - 6 ) !} (2 x)^{0} (5 y)^{6} : 15625 y^{6}

= 64 x^{6} + 960 x^{5} y + 6000 x^{4} y^{2} + 20000 x^{3} y^{3} + 37500 x^{2} y^{4} + 37500 x y^{5} + 15625 y^{6}

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