desarrollar (a-λ)(b-λ)(c-λ)(d-λ)(e-λ)

Solución

desarrollar

(a - λ) (b - λ) (c - λ) (d - λ) (e - λ)

e ab c d - aλb c d - e aλb c + a λ^{2} b c - e aλb d + a λ^{2} b d + e a λ^{2} b - a λ^{3} b - e aλ c d + a λ^{2} c d + e a λ^{2} c - a λ^{3} c + e a λ^{2} d - a λ^{3} d - e a λ^{3} + a λ^{4} - e λb c d + λ^{2} b c d + e λ^{2} b c - λ^{3} b c + e λ^{2} b d - λ^{3} b d - e λ^{3} b + λ^{4} b + e λ^{2} c d - λ^{3} c d - e λ^{3} c + λ^{4} c - e λ^{3} d + λ^{4} d + e λ^{4} - λ^{5}

Pasos de solución

(a - λ) (b - λ) (c - λ) (d - λ) (e - λ)

Expandir

(a - λ) (b - λ) : ab - aλ - λb + λ^{2}

= (ab - aλ - λb + λ^{2}) (c - λ) (d - λ) (e - λ)

Expandir

(ab - aλ - λb + λ^{2}) (c - λ) : ab c - aλb - aλ c + a λ^{2} - λb c + λ^{2} b + λ^{2} c - λ^{3}

= (ab c - aλb - aλ c + a λ^{2} - λb c + λ^{2} b + λ^{2} c - λ^{3}) (d - λ) (e - λ)

Expandir

(ab c - aλb - aλ c + a λ^{2} - λb c + λ^{2} b + λ^{2} c - λ^{3}) (d - λ) : ab c d - aλb c - aλb d + a λ^{2} b - aλ c d + a λ^{2} c + a λ^{2} d - a λ^{3} - λb c d + λ^{2} b c + λ^{2} b d - λ^{3} b + λ^{2} c d - λ^{3} c - λ^{3} d + λ^{4}

= (ab c d - aλb c - aλb d + a λ^{2} b - aλ c d + a λ^{2} c + a λ^{2} d - a λ^{3} - λb c d + λ^{2} b c + λ^{2} b d - λ^{3} b + λ^{2} c d - λ^{3} c - λ^{3} d + λ^{4}) (e - λ)

Expandir

(ab c d - aλb c - aλb d + a λ^{2} b - aλ c d + a λ^{2} c + a λ^{2} d - a λ^{3} - λb c d + λ^{2} b c + λ^{2} b d - λ^{3} b + λ^{2} c d - λ^{3} c - λ^{3} d + λ^{4}) (e - λ) : e ab c d - aλb c d - e aλb c + a λ^{2} b c - e aλb d + a λ^{2} b d + e a λ^{2} b - a λ^{3} b - e aλ c d + a λ^{2} c d + e a λ^{2} c - a λ^{3} c + e a λ^{2} d - a λ^{3} d - e a λ^{3} + a λ^{4} - e λb c d + λ^{2} b c d + e λ^{2} b c - λ^{3} b c + e λ^{2} b d - λ^{3} b d - e λ^{3} b + λ^{4} b + e λ^{2} c d - λ^{3} c d - e λ^{3} c + λ^{4} c - e λ^{3} d + λ^{4} d + e λ^{4} - λ^{5}

= e ab c d - aλb c d - e aλb c + a λ^{2} b c - e aλb d + a λ^{2} b d + e a λ^{2} b - a λ^{3} b - e aλ c d + a λ^{2} c d + e a λ^{2} c - a λ^{3} c + e a λ^{2} d - a λ^{3} d - e a λ^{3} + a λ^{4} - e λb c d + λ^{2} b c d + e λ^{2} b c - λ^{3} b c + e λ^{2} b d - λ^{3} b d - e λ^{3} b + λ^{4} b + e λ^{2} c d - λ^{3} c d - e λ^{3} c + λ^{4} c - e λ^{3} d + λ^{4} d + e λ^{4} - λ^{5}

e x p an d (sin (θ) - 2 r cos^{2} (θ)) d r + r cos (θ) (2 r sin (θ) + 1) d θ

e x p an d \frac{z ^{2} - 6 z + 8}{( z + 1 ) ( z + 2 )}

e x p an d 8 \cdot 6

e x p an d y^{\frac{1}{3}} (y^{\frac{1}{3}} - y^{\frac{3}{2}})

e x p an d (1 + e^{3 x})^{2}