Chapitre 5

Calcul littéral

Exercices complémentaires

Série A

1)
 Réduis, si cela est possible, les expressions suivantes.
a)
5x + 2x =
 ...... b)
3a . 2b =
 ...... c)
5 + 2x =
 ...... d)
– 3a + 2b =
 ......
 
– 3x + 4x =
 ......  
– 3b . (– 4a) =
 ......  
5 . 2x =
 ......  
– 3a + 5b =
 ......
 
– x + 5x =
 ......  
– 4x . 2x =
 ......  
5x – 2x =
 ......  
– 3a . (– 2a) =
 ......
 
– x – x =
 ......  
– 3x . (– x) =
 ......  
5x . (– 2x) =
 ......  
– 3a – 2a =
 ......
2x – 3x =
......  
– x . x =
 ......  
– 5x – 2x =
 ......  
– 3 – 2a =
 ......
                       
e)
2xy – 5xy =
   f)
7x2 + 5x2 =
   g)
2a – 5a2 =
   h)
– a2 – a2 =
 
 
ab + 3ab =
    
3x2 – 2x2 =
    
– b2 + 4b2 =
    
– a2 . (– a2) =
  
 
ab – 4ab =
    
7a2 + 5a2 =
    
– c2 – c2 =
    
– a2 + a2 =
  
 
3ab + 4ac =
    
– 4b2 – 2b2 =
    
c2 – 3c =
    
– a2 . a2 =
  
 
– ab – ab =
    
a2 – 3a2 =
    
5b2 – 5 =
    
– 2a . a2 =
  

2)
 Applique la distributivité et réduis les éventuels termes semblables.
5 . (2a + 3) =
............
(x + y) . (a + b) =
............
2a . (a + b) =
............
2a . (3b + 5c) =
............
(x + 3) . (y + 2) =
............
(3a + 2c) . a =
............
3x . (x + 5) =
............
(x + 4) . (x + 3) =
............
(3a + 1) . (2a + 1) =
............
(a + 3b) . 6a =
............
(2a + 1) . (3a + 2) =
............
(x + 2y) . (3x + y) =
............
(x + 2) . 2 =
............
(2x + 4) . (x + 1) =
............
(1 + 4x) . 2x =
............

3)

Mets le ou les facteurs communs en évidence.

 
a)
5x + 5y =
 ...... b)
12a – 8b =
 ...... c)
x2 + xy =
 ...... d)
8a2 – 12a =
......
 
xy + xz =
 ......  
15ab – 10ac =
 ......  
5x + 2x2 =
 ......  
– 15x + 10x2 =
 ......
 
5x + 10y =
 ......  
– 4a – 6c =
 ......  
8a2 + 12a =
 ......  
– 45a2 – 27a =
 ......
 
15a + 25b =
 ......  
– 2x + 4y =
 ......  
16x2 + 24x =
 ......  
8a – 16a2 =
 ......
 
6ab + 9ac =
 ......  
18a – 24b =
 ......  
3a2 + 13a =
 ......  
x2 – 3x =
 ......

4)
 Applique la distributivité et réduis les éventuels termes semblables.
5 . (2b – 4c) =
............
(a + b) . (c – d) =
............
(– 2a + 1) . (3 – 2x) =
............
– 3 . (– 2a + 3c) =
............
(2x – 3) . (y + 2) =
............
(5 – a) . (a – 3) =
............
2a . (3a – 5) =
............
(x – 5) . (3x – 1) =
............
(a – 1) . (1 + a) =
............
– 3x . (5 – 2x) =
............
(2a – 3) . (– 4a + 2) =
............
(x – 4) . (– 2 + x) =
............
– a . (a + 2) =
............
(2x – 7) . (x + 1) =
............
(– x + 3) . (– x – 1) =
............

5)
 Supprime les parenthèses et réduis les éventuels termes semblables.
2a – (3a – 5b) =
.............
a – (a – 3) + (5 – a) =
.............
– 4x + (2 – 3x) =
.............
2x + (x – 3) – (x + 2) =
.............
(– x + 2) – (5x + 3) =
.............
(– 3 + x) + (2x – 4) – (x + 6) =
.............
– (x – 2) + (– 2x – 4) =
.............
– (a – 3) + (– 2a – 5) – (–a + 2) =
.............
6a – (–a + 2) =
.............
6 – (2a – 5) + (– 2a + 4) =
.............

6)
 Applique la distributivité et réduis les termes semblables.
5a – 3 . (2a – 7) =
.............
3a – (2a + 3) . (5 – 2a) =
.............
(2x – y) + 5 . (x + y) =
.............
(2 + a) . (3 – a) + (5 – a) . (– a + 2) =
.............
5 . (a – 3) – 2 . (a + 5) =
.............
(x + 2) . (2x – 1) – (3x – 2) . (x – 4) =
.............
– 2 . (a – 3b) – 4 . (2b + 1) =
.............
5x + (x + 3) . (3x – 1) – (2x – 1) . (– x + 2) =
.............
5a . (a – 3) – 2 . (a + 5) =
.............
– (5x – 1) . (x + 1) + (– x – 1) . (– x + 2) =
.............

7) Réduis les expressions suivantes :

 


a)
a2 . 3a5 =
 ...... b)
(3a)2 =
 ...... c)
(3a2)2 =
 ...... d)
(– 2ab)3 =
 ......
 
x2 . 2x =
 ......  
(– 2a)3 =
 ......  
(– 5a3)2 =
 ......  
(– 3ab3)2 =
 ......
 
– 5a2 . 2a5 =
 ......  
(– 5b)2 =
 ......  
(– 10a2)3 =
 ......  
– 4x . 5x =
 ......
 
– a . (– 5a3) =
 ......  
(– 4d)3 =
 ......  
(– 2a4)3 =
 ......  
x3 . (– 3x2) =
 ......
 
– 3x . 2x2 =
 ......  
(2ab)5 =
 ......  
(– 7x7)2 =
 ......  
– b . (– 4b2) =
 ......

8) Réduis les expressions suivantes.

 

 

a)
4a3 . (– 4a3) =
 ...... b)
4a . 3 =
 ...... c)
3x2 + 5x =
 ...... d)
(– 3ab)2 =
 ......
 
a . (– 3a) =
 ......  
(– 4a)3 =
 ......  
3x2 . 5x =
 ......  
– 3 . (a + 2b) =
 ......
 
(– 3ab3)3=
 ......  
(– 4 + a) . 3 =
 ......  
(3x)2 . 5x =
 ......  
3 – (a + 2b) =
 ......
 
– 4a . (– 5a) =
 ......  
– 4 + a =
 ......  
(3 + x2) . 5x =
 ......  
– 3 . (2ab)2 =
 ......
 
– 3 . (ab3)3 =
 ......  
– 4a + 3a =
 ......  
(– 3x2) . 5x =
 ......  
(3 – a) . 2b =
 ......

9) Distribue et réduis les éventuels termes semblables.

 

 

a)
a2 . (4a4 + 3) =
 ...... b)
(x2 + 3) . (2x – 5) =
 ...... c)
– 4x2 . (5x + 4) + 2x . (x2 – 5) =
 ......
 
2a . (3a4 + a) =
 ......  
(3x – 4) . (x3 – 2)=
 ......  
2x . (– 3x + 7) – 2x2 . (3 + x) =
......
 
– 4x . (2x + 1) =
 ......  
(2x3 – 5) . (– x3 + 2) =
 ......  
– 3x . (2x2 – 1) – (x2 – 1) . (x + 3) =
 ......
 
3a . (a – 4a2) =
 ......  
(– x2 + 1) . (x2 + 4) =
 ......  
– (3x – 4) . (x2 – 2) – x2 . (– 3 + x) =
 ......
 
– 2x . (x3 – 2x) =
 ......  
(– x – 3) . (– 3x2 + 5x) =
 ......  
– 4 . (x2 – 1) – (2x – 1) . (2x + 1) =
 ......

10) Vrai ou faux ? Si c'est faux corrige le second membre de l'égalité.

 

 

5 . (a + 5)
=
5 a + 25
a2 . a5
=
a10
3a4. (– a2)
=
– 3 a2
4 . (a – 5)
=
4 a – 1
(a3)2
=
a9
(– 4 a4)2
=
16 a8
2 . (a + 4)
=
2 a + 6
a . a5
=
a6
(– 3 a3)3
 =
– 9 a9
7. (a – 7)
=
7 a
(3 a)2
=
6 a2
7 . (ab)2
=
7 ab2
6 . (a – 6)
=
6 a – 36
(– 10 a)3
 =
1000 a3
(7 ab)2
=
49 a2b2

11) Complète les égalités.

 

 

a)
15 a = 5a +
...... b)
6 a = 6 a +
...... c)
a2 = a .
...... d)
9 a2 = 9 a .
......
 
20 a = 5a .
......  
5 a = 5 a .
......  
3 a2 = a .
......  
5 a2 = – 5 a .
......
 
8 a = – 4 .
......  
2 a = a +
......  
5 5a3= a .
......  
– 8 a2 = – 4 .
......
 
14 a = 18 a –
......  
4 a = 5 a –
......  
3 a2 = a2 +
......  
7 a2 = a2 +
......
 
– 2 a = – a –
 ......  
– 4 a = 4 a .
......  
– 4 a2 = 5 a2 –
......  
– a 2 = a2 +
......

Vos remarques sont les bienvenues.