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desarrollar (-1/20 (x-50))^2

Solución

desarrollar

(- \frac{1}{20} (x - 50))^{2}

Solución

\frac{x ^{2}}{400} - \frac{x}{4} + \frac{25}{4}

Pasos de solución

(- \frac{1}{20} (x - 50))^{2}

Aplicar las leyes de los exponentes:

(- a)^{n} = a^{n},

si

n

es par

(- \frac{1}{20} (x - 50))^{2} = (\frac{1}{20} (x - 50))^{2}

= (\frac{1}{20} (x - 50))^{2}

Aplicar las leyes de los exponentes:

(a \cdot b)^{n} = a^{n} b^{n}

= (\frac{1}{20})^{2} (x - 50)^{2}

Aplicar las leyes de los exponentes:

(\frac{a}{b})^{c} = \frac{a ^{c}}{b ^{c}}

(\frac{1}{20})^{2} = \frac{1 ^{2}}{2 0 ^{2}}

= \frac{1 ^{2}}{2 0 ^{2}} (x - 50)^{2}

Aplicar la regla

1^{a} = 1

1^{2} = 1

= \frac{1}{2 0 ^{2}} (x - 50)^{2}

(x - 50)^{2} = x^{2} - 100 x + 2500

= \frac{1}{2 0 ^{2}} (x^{2} - 100 x + 2500)

2 0^{2} = 400

= \frac{1}{400} (x^{2} - 100 x + 2500)

Aplicar la siguiente regla de productos notables

= \frac{1}{400} x^{2} + \frac{1}{400} (- 100 x) + \frac{1}{400} \cdot 2500

Aplicar las reglas de los signos

+ (- a) = - a

= \frac{1}{400} x^{2} - 100 \cdot \frac{1}{400} x + 2500 \cdot \frac{1}{400}

Simplificar

\frac{1}{400} x^{2} - 100 \cdot \frac{1}{400} x + 2500 \cdot \frac{1}{400} : \frac{x ^{2}}{400} + \frac{- x + 25}{4}

= \frac{x ^{2}}{400} + \frac{- x + 25}{4}

Aplicar las propiedades de las fracciones:

\frac{a \pm b}{c} = \frac{a}{c} \pm \frac{b}{c}

\frac{- x + 25}{4} = - \frac{x}{4} + \frac{25}{4}

= \frac{x ^{2}}{400} - \frac{x}{4} + \frac{25}{4}

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