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Popular Álgebra >

desarrollar (x+dx)^5

Solución

desarrollar

(x + d x)^{5}

Solución

x^{5} + 5 x^{4} d x + 10 x^{3} d x^{2} + 10 x^{2} d x^{3} + 5 x d x^{4} + d x^{5}

Pasos de solución

(x + d x)^{5}

Aplicar el teorema del binomio:

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

a = x, b = d x

= i = 0 \sum 5 (i 5) x^{(5 - i)} d x^{i}

Expandir sumatorio

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

Simplificar

\frac{5 !}{0 ! ( 5 - 0 ) !} x^{5} d x^{0} : x^{5}

Simplificar

\frac{5 !}{1 ! ( 5 - 1 ) !} x^{4} d x^{1} : 5 x^{4} d x

Simplificar

\frac{5 !}{2 ! ( 5 - 2 ) !} x^{3} d x^{2} : 10 x^{3} d x^{2}

Simplificar

\frac{5 !}{3 ! ( 5 - 3 ) !} x^{2} d x^{3} : 10 x^{2} d x^{3}

Simplificar

\frac{5 !}{4 ! ( 5 - 4 ) !} x^{1} d x^{4} : 5 x d x^{4}

Simplificar

\frac{5 !}{5 ! ( 5 - 5 ) !} x^{0} d x^{5} : d x^{5}

= x^{5} + 5 x^{4} d x + 10 x^{3} d x^{2} + 10 x^{2} d x^{3} + 5 x d x^{4} + d x^{5}

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desarrollar (x+5)(x+Δx)^2-1

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