📘 10 Exercices : Développement et Factorisation
5 questions par exercice • 1ère Année Collège (1AC)
✏️ Exercice 1 : Développer
1. \( 2(x + 5) = \) →
2. \( 3(y – 4) = \) →
3. \( 4(2a + 1) = \) →
4. \( 5(b – 3) = \) →
5. \( 6(x + 2) = \) →
1. \( 2(x + 5) = 2x + 10 \)
2. \( 3(y – 4) = 3y – 12 \)
3. \( 4(2a + 1) = 8a + 4 \)
4. \( 5(b – 3) = 5b – 15 \)
5. \( 6(x + 2) = 6x + 12 \)
→ On applique : \( k(a \pm b) = ka \pm kb \)
✏️ Exercice 2 : Factoriser
1. \( 6x + 12 = \) →
2. \( 8y – 16 = \) →
3. \( 5a + 25 = \) →
4. \( 4b – 20 = \) →
5. \( 9x + 18 = \) →
Chercher le facteur commun :
1. 6 divise 6x et 12 → \( 6(x + 2) \)
2. 8 divise 8y et 16 → \( 8(y – 2) \)
3. 5 divise 5a et 25 → \( 5(a + 5) \)
4. 4 divise 4b et 20 → \( 4(b – 5) \)
5. 9 divise 9x et 18 → \( 9(x + 2) \)
✏️ Exercice 3 : Compléter
1. \( 3(x + \ldots) = 3x + 18 \) →
2. \( 5(y – \ldots) = 5y – 25 \) →
3. \( \ldots(a + 4) = 8a + 32 \) →
4. \( 7(\ldots + 3) = 7b + 21 \) →
5. \( \ldots(x – 6) = 9x – 54 \) →
1. \( 3 \times \ldots = 18 \Rightarrow \ldots = 6 \)
2. \( 5 \times \ldots = 25 \Rightarrow \ldots = 5 \)
3. \( \ldots \times 4 = 32 \Rightarrow \ldots = 8 \)
4. \( 7 \times \ldots = 7b \Rightarrow \ldots = b \)
5. \( \ldots \times 6 = 54 \Rightarrow \ldots = 9 \)
✏️ Exercice 4 : Vrai ou Faux
1. \( 4(x + 3) = 4x + 12 \) →
2. \( 2(y – 5) = 2y – 5 \) →
3. \( 6a + 18 = 6(a + 3) \) →
4. \( 5(b – 4) = 5b – 20 \) →
5. \( 3x + 9 = 3(x + 6) \) →
1. \( 4x + 12 \) → correct
2. \( 2y – 10 \) → pas \( -5 \)
3. \( 6a + 18 = 6(a + 3) \) → correct
4. \( 5b – 20 \) → correct
5. \( 3x + 9 = 3(x + 3) \), pas \( +6 \)
✏️ Exercice 5 : Développer
1. \( 2(4x + 3) = \) →
2. \( 3(2y – 5) = \) →
3. \( 4(3a + 2) = \) →
4. \( 5(2b – 4) = \) →
5. \( 6(x + 1) = \) →
1. \( 2 \times 4x = 8x \), \( 2 \times 3 = 6 \) → \( 8x + 6 \)
2. \( 3 \times 2y = 6y \), \( 3 \times 5 = 15 \) → \( 6y – 15 \)
3. \( 4 \times 3a = 12a \), \( 4 \times 2 = 8 \) → \( 12a + 8 \)
4. \( 5 \times 2b = 10b \), \( 5 \times 4 = 20 \) → \( 10b – 20 \)
5. \( 6 \times x = 6x \), \( 6 \times 1 = 6 \) → \( 6x + 6 \)
✏️ Exercice 6 : Factoriser
1. \( 10x + 20 = \) →
2. \( 12y – 36 = \) →
3. \( 7a + 14 = \) →
4. \( 8b – 24 = \) →
5. \( 5x + 30 = \) →
Chercher le facteur commun :
1. 10 → \( 10(x + 2) \)
2. 12 → \( 12(y – 3) \)
3. 7 → \( 7(a + 2) \)
4. 8 → \( 8(b – 3) \)
5. 5 → \( 5(x + 6) \)
✏️ Exercice 7 : Problèmes
1. Le double de \( x + 7 \) →
2. Le triple de \( y – 2 \) →
3. \( 4 \times (a + 5) = \) →
4. Factoriser \( 3x + 12 \) →
5. Développer \( 5(2x – 1) \) →
1. \( 2 \times (x + 7) = 2(x + 7) \)
2. \( 3 \times (y – 2) = 3(y – 2) \)
3. \( 4a + 20 \)
4. Facteur commun 3 → \( 3(x + 4) \)
5. \( 5 \times 2x = 10x \), \( 5 \times 1 = 5 \) → \( 10x – 5 \)
✏️ Exercice 8 : Équivalence
1. \( 2x + 8 = \) →
2. \( 3x – 9 = \) →
3. \( 4(x + 2) = \) →
4. \( 5(3y – 1) = \) →
5. \( 6a + 18 = \) →
1. Facteur commun 2 → \( 2(x + 4) \)
2. Facteur commun 3 → \( 3(x – 3) \)
3. \( 4x + 8 \)
4. \( 15y – 5 \)
5. Facteur commun 6 → \( 6(a + 3) \)
✏️ Exercice 9 : Compléter l’expression
1. \( 3(\ldots + 4) = 3x + 12 \) →
2. \( \ldots(y – 3) = 6y – 18 \) →
3. \( 5(2a + \ldots) = 10a + 25 \) →
4. \( 4(\ldots – 2) = 4b – 8 \) →
5. \( \ldots(x + 5) = 7x + 35 \) →
1. \( 3 \times \ldots = 3x \Rightarrow \ldots = x \)
2. \( \ldots \times 3 = 18 \Rightarrow \ldots = 6 \)
3. \( 5 \times \ldots = 25 \Rightarrow \ldots = 5 \)
4. \( 4 \times \ldots = 4b \Rightarrow \ldots = b \)
5. \( \ldots \times 5 = 35 \Rightarrow \ldots = 7 \)
✏️ Exercice 10 : Révision Générale
1. \( 2(x + 9) = \) →
2. \( 7y – 21 = \) →
3. \( 3(4a – 2) = \) →
4. \( 8x + 32 = \) →
5. \( 5(b – 6) = \) →
1. \( 2x + 18 \)
2. Facteur commun 7 → \( 7(y – 3) \)
3. \( 12a – 6 \)
4. Facteur commun 8 → \( 8(x + 4) \)
5. \( 5b – 30 \)
