Exercice 3
Développer les
expressions suivantes en utilisant l’identité remarquable (a + b)² = a² + 2ab
+ b² :
|
A = |
(x + 2)² |
= |
|
|
B = |
(3 + x)² |
= |
|
|
C = |
(x + 5)² |
= |
|
|
D = |
(2x + 1)² |
= |
|
|
E = |
(1 +
3x)² |
= |
|
|
F = |
(3x +
2)² |
= |
|
|
G = |
(5x +
3)² |
= |
|
|
H = |
(x² +
1)² |
= |
|
|
I = |
(3 + 4x)² |
= |
|
|
J = |
(3x² + 4)² |
= |
|
Exercice 4
Développer les
expressions suivantes en utilisant l’identité remarquable (a – b)² = a² – 2ab
+ b² :
|
A = |
(x – 2)² |
= |
|
|
B = |
(5 – x)² |
= |
|
|
C = |
(1 –
3x)² |
= |
|
|
D = |
(3 – x)² |
= |
|
|
E = |
(2x –
1)² |
= |
|
|
F = |
(3 –
5x)² |
= |
|
|
G = |
(3x –
2)² |
= |
|
|
H = |
(4x –
3)² |
= |
|
|
I = |
(1 – x²)² |
= |
|
|
J = |
(4 – 3x²)² |
= |
|
Exercice 5
Développer les
expressions suivantes en utilisant l’identité remarquable (a + b)(a – b) = a²
– b² :
|
A = |
(x +2)(x
– 2) |
= |
|
|
B = |
(5 – x)(5 +
x) |
= |
|
|
C = |
(x + 3)(x –
3) |
= |
|
|
D = |
(3x – 1)(3x
+ 1) |
= |
|
|
E = |
(2x +
1)(2x – 1) |
= |
|
|
F = |
(5 +
3x)(5 – 3x) |
= |
|
|
G = |
(3x –
2)(3x + 2) |
= |
|
|
H = |
(3 +
4x)(3 – 4x) |
= |
|
|
I = |
(x3
+ 1)(x3 – 1) |
= |
|
|
J = |
(4x² + 3)(4x² – 3) |
= |
|
Exercice 6
Développer les
expressions suivantes en utilisant l’identité remarquable qui convient :
|
A = |
(x + 4)² |
= |
|
|
B = |
(2 - x)² |
= |
|
|
C = |
(x +
1)(x – 1) |
= |
|
|
D = |
(2x + 1)² |
= |
|
|
E = |
(3 –
2x)² |
= |
|
|
F = |
(7x +
5)² |
= |
|
|
G = |
(5x +
6)(5x – 6) |
= |
|
|
H = |
(4 –
8x)² |
= |
|
|
I = |
(3 + 4x)(3
+ 4x) |
= |
|
|
J = |
(3 + x)(x – 3) |
= |
|
Exercice 7
a.
Développer et réduire :
|
A = (x +
1)² + (x – 3)² |
|
B = (3 –
x)² + (x + 5)² |
|
C = (x –
2)² + (x + 4)(x – 4) |
|
D = (x +
1)(x – 1) + (x + 4)² |
|
E = (x –
5)² + (2x + 7)(2x – 7) |
b.
Développer et réduire :
|
A = (2x
+ 1)² – (x + 3)² |
|
B = (2x +
3)² – (x – 7)(x + 7) |
|
C = (x +
2)(x – 2) – (x – 3)² |
|
D = (x –
5)² – (2x – 7)(x – 5) |
|
E = (3x +
1)(x – 2) – (2x – 3)² |