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Popular Álgebra >

desarrollar (2x+y)^7

Solución

desarrollar

(2 x + y)^{7}

Solución

128 x^{7} + 448 x^{6} y + 672 x^{5} y^{2} + 560 x^{4} y^{3} + 280 x^{3} y^{4} + 84 x^{2} y^{5} + 14 x y^{6} + y^{7}

Pasos de solución

(2 x + y)^{7}

Aplicar el teorema del binomio:

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

a = 2 x, b = y

= i = 0 \sum 7 (i 7) (2 x)^{(7 - i)} y^{i}

Expandir sumatorio

= \frac{7 !}{0 ! ( 7 - 0 ) !} (2 x)^{7} y^{0} + \frac{7 !}{1 ! ( 7 - 1 ) !} (2 x)^{6} y^{1} + \frac{7 !}{2 ! ( 7 - 2 ) !} (2 x)^{5} y^{2} + \frac{7 !}{3 ! ( 7 - 3 ) !} (2 x)^{4} y^{3} + \frac{7 !}{4 ! ( 7 - 4 ) !} (2 x)^{3} y^{4} + \frac{7 !}{5 ! ( 7 - 5 ) !} (2 x)^{2} y^{5} + \frac{7 !}{6 ! ( 7 - 6 ) !} (2 x)^{1} y^{6} + \frac{7 !}{7 ! ( 7 - 7 ) !} (2 x)^{0} y^{7}

Simplificar

\frac{7 !}{0 ! ( 7 - 0 ) !} (2 x)^{7} y^{0} : 128 x^{7}

Simplificar

\frac{7 !}{1 ! ( 7 - 1 ) !} (2 x)^{6} y^{1} : 448 x^{6} y

Simplificar

\frac{7 !}{2 ! ( 7 - 2 ) !} (2 x)^{5} y^{2} : 672 x^{5} y^{2}

Simplificar

\frac{7 !}{3 ! ( 7 - 3 ) !} (2 x)^{4} y^{3} : 560 x^{4} y^{3}

Simplificar

\frac{7 !}{4 ! ( 7 - 4 ) !} (2 x)^{3} y^{4} : 280 x^{3} y^{4}

Simplificar

\frac{7 !}{5 ! ( 7 - 5 ) !} (2 x)^{2} y^{5} : 84 x^{2} y^{5}

Simplificar

\frac{7 !}{6 ! ( 7 - 6 ) !} (2 x)^{1} y^{6} : 14 x y^{6}

Simplificar

\frac{7 !}{7 ! ( 7 - 7 ) !} (2 x)^{0} y^{7} : y^{7}

= 128 x^{7} + 448 x^{6} y + 672 x^{5} y^{2} + 560 x^{4} y^{3} + 280 x^{3} y^{4} + 84 x^{2} y^{5} + 14 x y^{6} + y^{7}

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