desarrollar (x-y^2)^6

Solución

desarrollar

(x - y^{2})^{6}

x^{6} - 6 x^{5} y^{2} + 15 x^{4} y^{4} - 20 x^{3} y^{6} + 15 x^{2} y^{8} - 6 x y^{10} + y^{12}

Pasos de solución

(x - y^{2})^{6}

Aplicar el teorema del binomio:

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

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

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

Expandir sumatorio

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

Simplificar

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

Simplificar

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

Simplificar

\frac{6 !}{2 ! ( 6 - 2 ) !} x^{4} (- y^{2})^{2} : 15 x^{4} y^{4}

Simplificar

\frac{6 !}{3 ! ( 6 - 3 ) !} x^{3} (- y^{2})^{3} : - 20 x^{3} y^{6}

Simplificar

\frac{6 !}{4 ! ( 6 - 4 ) !} x^{2} (- y^{2})^{4} : 15 x^{2} y^{8}

Simplificar

\frac{6 !}{5 ! ( 6 - 5 ) !} x^{1} (- y^{2})^{5} : - 6 x y^{10}

Simplificar

\frac{6 !}{6 ! ( 6 - 6 ) !} x^{0} (- y^{2})^{6} : y^{12}

= x^{6} - 6 x^{5} y^{2} + 15 x^{4} y^{4} - 20 x^{3} y^{6} + 15 x^{2} y^{8} - 6 x y^{10} + y^{12}

s im pl i f y - 8 \cdot (- 2)

s im pl i f y (\frac{2}{5})^{3} \cdot (\frac{2}{5})^{2}

s im pl i f y \frac{25}{1000}

s im pl i f y \frac{3 - 4 i}{- 2 + 2 i}

e x p an d (4 x^{2} + y)^{2}