desarrollar (-3x^2+2y)^5

Solución

desarrollar

(- 3 x^{2} + 2 y)^{5}

- 243 x^{10} + 810 x^{8} y - 1080 x^{6} y^{2} + 720 x^{4} y^{3} - 240 x^{2} y^{4} + 32 y^{5}

Pasos de solución

(- 3 x^{2} + 2 y)^{5}

Aplicar el teorema del binomio:

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

a = - 3 x^{2}, b = 2 y

= i = 0 \sum 5 (i 5) (- 3 x^{2})^{(5 - i)} (2 y)^{i}

Expandir sumatorio

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

Simplificar

\frac{5 !}{0 ! ( 5 - 0 ) !} (- 3 x^{2})^{5} (2 y)^{0} : - 243 x^{10}

Simplificar

\frac{5 !}{1 ! ( 5 - 1 ) !} (- 3 x^{2})^{4} (2 y)^{1} : 810 x^{8} y

Simplificar

\frac{5 !}{2 ! ( 5 - 2 ) !} (- 3 x^{2})^{3} (2 y)^{2} : - 1080 x^{6} y^{2}

Simplificar

\frac{5 !}{3 ! ( 5 - 3 ) !} (- 3 x^{2})^{2} (2 y)^{3} : 720 x^{4} y^{3}

Simplificar

\frac{5 !}{4 ! ( 5 - 4 ) !} (- 3 x^{2})^{1} (2 y)^{4} : - 240 x^{2} y^{4}

Simplificar

\frac{5 !}{5 ! ( 5 - 5 ) !} (- 3 x^{2})^{0} (2 y)^{5} : 32 y^{5}

= - 243 x^{10} + 810 x^{8} y - 1080 x^{6} y^{2} + 720 x^{4} y^{3} - 240 x^{2} y^{4} + 32 y^{5}

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