desarrollar 2(x+piy)^5

Solución

desarrollar

2 (x + π y)^{5}

2 x^{5} + 10 π x^{4} y + 20 π^{2} x^{3} y^{2} + 20 π^{3} x^{2} y^{3} + 10 π^{4} x y^{4} + 2 π^{5} y^{5}

Pasos de solución

2 (x + π y)^{5}

(x + π y)^{5} = x^{5} + 5 π x^{4} y + 10 π^{2} x^{3} y^{2} + 10 π^{3} x^{2} y^{3} + 5 π^{4} x y^{4} + π^{5} y^{5}

= 2 (x^{5} + 5 π x^{4} y + 10 π^{2} x^{3} y^{2} + 10 π^{3} x^{2} y^{3} + 5 π^{4} x y^{4} + π^{5} y^{5})

Aplicar la siguiente regla de productos notables

= 2 x^{5} + 2 \cdot 5 π x^{4} y + 2 \cdot 10 π^{2} x^{3} y^{2} + 2 \cdot 10 π^{3} x^{2} y^{3} + 2 \cdot 5 π^{4} x y^{4} + 2 π^{5} y^{5}

Simplificar

2 x^{5} + 2 \cdot 5 π x^{4} y + 2 \cdot 10 π^{2} x^{3} y^{2} + 2 \cdot 10 π^{3} x^{2} y^{3} + 2 \cdot 5 π^{4} x y^{4} + 2 π^{5} y^{5} : 2 x^{5} + 10 π x^{4} y + 20 π^{2} x^{3} y^{2} + 20 π^{3} x^{2} y^{3} + 10 π^{4} x y^{4} + 2 π^{5} y^{5}

= 2 x^{5} + 10 π x^{4} y + 20 π^{2} x^{3} y^{2} + 20 π^{3} x^{2} y^{3} + 10 π^{4} x y^{4} + 2 π^{5} y^{5}

e x p an d (1 + e^{x}) e^{2 x}

e x p an d \frac{( k + 1 ) ^{2} ( k + 2 ) ^{2} ( 2 k ^{2} + 6 k + 3 )}{12}

e x p an d \frac{2 π ( 7 17 + 1 )}{3}

e x p an d \frac{\frac{d}{d x} ( ( 3 x ^{2} + 9 ) ( 5 x - 3 ) )}{6 x - 7}

e x p an d y (sin (2 0^{\circ}) - 8195 cos (2 0^{\circ}))