Exercices complémentaires |
Série A4)
Applique
la distributivité et réduis les éventuels termes
semblables. |
5
.
(2b – 4c) |
= 5 . 2b – 5 . 4c |
| = 10b – 20c | |
–
3 .
(– 2a + 3c) |
= (– 3) . (– 2a) + (– 3) . 3c |
| = 6a – 9c | |
2a
.
(3a – 5) |
= 2a . 3a – 2a . 5 |
| = 6a2 – 10a | |
–
3x .
(5 – 2x) |
= (– 3x) . 5 – (– 3x) . 2x |
| = –15x + 6x2 | |
–
a .
(a + 2) |
= (– a) . a + (– a) . 2 |
| = – a2 – 2a | |
(a
+ b) .
(c – d)
|
= a . c +a . (– d) + b . c + b . (– d) |
| = ac – ad + bc – bd | |
(2x
– 3) .
(y + 2)
|
= 2x . y + 2x . 2 + (– 3) . y + (– 3) . 2 |
| = 2xy + 4x – 3y – 6 | |
(x
– 5) .
(3x – 1)
|
= x . 3x + x . (– 1) + (– 5) . 3x + (– 5) . (– 1) |
| = 3x2 + (– x) + (– 15 x) + 5 | |
| = 3x2 – 16 x + 5 | |
(2a
– 3) .
(– 4a
+ 2) |
= 2a . (– 4a) + 2a . 2 + ( – 3) . (– 4a) + ( – 3) . 2 |
| = –8a2 + 4a + 12a – 6 | |
| = –8a2 + 16a – 6 | |
(2x
– 7) .
(x + 1)
|
= 2x . x + 2x . 1 + ( – 7) . x + ( – 7) . 1 |
| = 2x2 + 2x – 7x – 7 | |
| = 2x2 – 5x – 7 | |
(–
2a + 1)
. (3
– 2x) |
= (– 2a) . 3 + (– 2a) . (– 2x) + 1 . 3 + 1 . (– 2x) |
| = – 6a + 4ax + 3 – 2x | |
(5
– a) .
(a –
3) |
= 5 . a + 5 . (– 3) + (– a) . a + (– a) . (– 3) |
| = 5a – 15 – a2 + 3a | |
| = – a2 + 8a – 15 | |
(a
– 1) .
(1 + a)
|
= a . 1 + a . a + (– 1) . 1 + (– 1) . a |
| = a + a2 – 1 – a | |
| = a2 – 1 | |
(x
– 4) .
(–
2 + x)
|
= x . (– 2) +x . x + (– 4) . (– 2) + (– 4) . x |
| = – 2x + x2 + 8 + (– 4x) | |
| = x2 – 6x + 8 | |
(–
x +
3)
. (–
x – 1)
|
= (– x) . (– x) +(– x) . (– 1) + 3 . (– x) + 3 . (– 1) |
| = x2 + x – 3x – 3 | |
| = x2 – 2x – 3 |