Calcul littéral - 4e

Développements par simple distributivité

Exercice 1 : 1 variable, fractions, 2 termes

Développer l'expression suivante : \[ \dfrac{-2}{5}n\left(\dfrac{3}{4}n -5n\right) + 3n\left(\dfrac{-5}{2}n -4n\right) \]

Exercice 2 : Développement de ax - b + cx - d(e*x + f)

Développer l'expression suivante : \[ 9x - 8 + 6x - 3\left(-9x + 5\right) \]

Exercice 3 : Développement de ax(bx+c) (fractions qui se simplifient))

Développer l'expression suivante : \[ \dfrac{5}{3}x\left(\dfrac{12}{-10}x + \dfrac{9}{-45}\right) \]

Exercice 4 : Comprendre le fonctionnement d'un algorithme

L'algorithme suivant représente un calcul :
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Vous pouvez tenter de le modifier pour le comprendre.

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Si on donne à \( x \) la valeur \(6N\) conjecturer la valeur de \( total \) à la fin de l'algorithme.
Exemple de réponse : \(6N + 1\)

Si on donne à \( x \) la valeur \(3N\) conjecturer la valeur de \( total \) à la fin de l'algorithme.
Exemple de réponse : \(3N + 1\)

Si on donne à \( x \) la valeur \(-5N\) conjecturer la valeur de \( total \) à la fin de l'algorithme.
Exemple de réponse : \(-5N + 1\)

Indiquer l'expression littérale donnant \( total \).
Exemple de réponse : \(0.01x + 1\)

Exercice 5 : Développement et réduction de ax(bx+c)+d(ex+f) (entiers relatifs)

Développer et réduire l'expression suivante : \[ 8\left(9x + 9\right) + 3x\left(5x + 5\right) \]

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