Chapitre 7Les produits remarquables |
| a) | Applique la bonne formule. |
|
(a
+ b)2 =
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(4
a – 2 b)2 =
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(3
– a2)2 =
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(x
– 5) . (5 + x) =
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(a
– b) . (a + b) =
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(x3
+ 1) . (x3 – 1) =
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(2
a + 3) . (2 a – 3) =
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(3
x – 2 y)2 =
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(5
– b)2 =
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(a
+ 4) 2 =
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(5
x + 2 y)2 =
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(2
– x2) . (x2
+ 2) =
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(2
x + 3 y2) . (3 y2
– 2 x) =
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(3
a3 – 2 b2)2 =
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| b) | Identifie l'exercice en précisant s'il s'agit d'une double distributivité (DD), d'une somme au carré (SC), d'une différence au carré (DC) ou d'un produit de deux binômes conjugués (BC). Puis effectue. |
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| c) | Applique les produits remarquables pour calculer. |
| 1052 = .............................................................................................................................. |
| 412 = .............................................................................................................................. |
| 692 = .............................................................................................................................. |
| 39 . 41 = .............................................................................................................................. |
| 98 . 102 = .............................................................................................................................. |
| 45 . 55 = .............................................................................................................................. |
| 57 . 63 = .............................................................................................................................. |
| d) | En calculant séparément chaque membre, vérifie si les égalités suivantes sont vraies. |
| (7
. 8)2 = 7 .
82 |
(7
. 8)2 = 72
. 82 |
(7
+ 8)2 = 72 + 82 |
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| (2
+ 3)3 = 23 + 33 |
(2
. 3)3 = 23 .
33 |
(2
. 3)3 = 2 .
33 |
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| (7
+ 3) . (7 – 3) = 49 –
9 |
(3
– 7) . (7 – 3) = (7
– 3)2 |
(7
+ 3) . (7 + 3) = 49 + 9 |
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| En t'inspirant des exercices ci–dessus, complète par = ou <>. |
| (a
+ b)2 |
...... |
a2 + b2 | (a
+ b) . (a – b) |
...... |
a2 – b2 | (a
+ b)3 |
...... |
a3 + b3 |
| (a
. b)2 |
...... |
a2 . b2 | (a
+ b) . (a + b) |
...... |
a2 + b2 | (a
. b)3 |
...... |
a3 . b3 |
| (a
. b)2 |
...... |
a . b2 | (a
– b) . (b – a) |
...... |
(a – b)2 | (a
. b)3 |
...... |
a . b3 |
| e) | Complète par = ou <> |
| x2
– y2 |
...... |
y2 – x2 | (x
– y) . (x – y) |
...... |
x2 + y2 |
| (x
+ 5) . (x – 5) |
...... |
x2 – 10 | (2x
– y)2 |
...... |
(x – 2y)2 |
| (x
– y)2 |
...... |
(y – x)2 | (x
+ y)2 |
...... |
(–x – y)2 |
| xy2 |
...... |
x2y | (x
– y)2 |
...... |
x2 – y2 |
| x2
+ y2 |
...... |
(x + y)2 | x2y2 |
...... |
(xy)2 |
| f) | Ecris sans parenthèses. |
| (5x)2
= |
................... |
(x
+ 2) . (x – 2) = |
................... |
| 5
. (x + 2) = |
................... |
(x
+ 3) . (x – 2) = |
................... |
| (5
+ x)2 = |
................... |
(x
+ 3) . (x + 3) = |
................... |
| 5
– (x – 2) = |
................... |
(x
+ 3) – (x – 3) = |
................... |
| (5
– x) . 2 = |
................... |
(x
– 3) . (3 – x) = |
................... |
Vos
remarques sont les bienvenues.
