| a) | Distribue et réduis les termes semblables. |
| (a
– 5) . (a + 5) |
= a . a + a . 5 + (–5) . a + (–5) . 5 |
| = a2 + 5 a + (–5 a) + (25) | |
| = a2 – 25 | |
| (a
– 4) . (a + 3) |
= a . a + a . 3 + (– 4) . a + (– 4) . 3 |
| = a2 + 3 a + (– 4 a)+ (– 12) | |
| = a2 – a – 12 | |
| (3
a + 2) . (3 a – 2) |
= 3 a . 3 a + 3 a . (– 2) + 2 . 3 a + 2 . (– 2) |
| = 9 a2 – 6 a + 6 a – 4 | |
| = 9 a2 – 4 | |
|
(a2 – 3) .
(a2 + 3) |
= a2 . a2 + a2 . 3 + (– 3) . a2 + (– 3) . 3 |
| = a4 + 3 a2 + (–3 a2) – 9 | |
| = a4 – 9 | |
| (2
a + 3) . (2 a – 3) |
= 2 a . 2 a + 2 a . (– 3) + 3 . 2 a + 3 . (– 3) |
| = 4 a2 + (– 6 a) + 6 a + (– 9) | |
| = 4 a2 – 9 | |
| (3
a – b) . (b + 3 a) |
= 3 a . b + 3 a . 3 a + (– b) . b + (– b) . 3 a |
| = 3 ab + 9 a2 + (– b2) + (– 3ab) | |
| = 9 a2 – b2 | |
| (–
a – 4) . (– a
+ 5) |
= (–a) . (–a) + (–a) . 5 + (– 4) . (–a) + (– 4) . 5 |
| = a2 + (– 5 a) + 4 a + (– 20) | |
| = a2 – a – 20 | |
| (–
5 a + 2) . (5 a + 2) |
= (– 5 a) . 5 a + (– 5 a) . 2 + 2 . 5 a + 2 . 2 |
| = (– 25 a2) + (– 10 a) + 10 a + 4 | |
| = – 25 a2 + 4 | |
| (a3 – 1) . (a3 + 1) |
= a3 . a3 + a3 . 1 + (– 1) . a3 + (– 1) . 1 |
| = a6 + a3 + (– a3) + (– 1) | |
| = a6 – 1 | |
| (a
+ 3) . (a + 3) |
= a . a + a . 3 + 3 . a + 3 . 3 |
| = a2 + 3 a + 3 a + 9 | |
| = a2 + 6 a + 9 | |