Exercices complémentaires

Série A

9) Distribue et réduis les éventuels termes semblables.
a2 . (a4 + 3)
 = a2 . 4a4 + a2 . 3
= 4a6 + 3a2
 
2a . (3a4 + a)
= 2a . 3a4 + 2a . a
= 6a5 + 2a2
   
– 4x . (2x + 1)
 = (– 4x) . 2x + (– 4x) .1 =
  = – 8 x2 – 4x
   
3a . (a – 4a2)
 = 3a  . a – 3a  . 4a2
  = 3 a2 – 12 a3
   
– 2x . (x3 – 2x)
 = (– 2x) . x3 – (– 2x) . 2x
  = – 2x4 + 4x2
   
(x2 + 3) . (2x – 5)
= x2 . 2x + x2 . (– 5) + 3 . 2x + 3 . (– 5)
  = 2x3 – 5 x2 + 6x – 15
   
(3x – 4) . (x3 – 2)
= 3x . x3 + 3x . (– 2) + (– 4) . x3 + (– 4) . (– 2)
  = 3x4 – 6x – 4x3 + 8
   
(2x3 – 5) . (– x3 + 2)
= 2x3. (– x3) + 2x3. 2 + (– 5) . (– x3) + (– 5) . 2
  = – 2x6 + 4x3 + 5 x3 – 10
  = – 2x6 + 9x3 – 10
   
(– x2 + 1) . (x2 + 4)
= (– x2) . x2 + (– x2) . 4 + 1 . x2 + 1 . 4
  = – x4 – 4x2 + x2 + 4
  = – x4 – 3x2 + 4
   
(– x – 3) . (– 3 x2 + 5x)
= (– x) . (– 3 x2) + (– x) . 5x + (– 3) . (– 3 x2) + (– 3) . 5x
  = 3 x3 – 5x2 + 9 x2 – 15x
  = 3 x3 + 4 x2 – 15x
   
– 4x2 . (5x + 4) + 2x . (x2 – 5)
= [– 4x2 . (5x + 4)] + [2x . (x2 – 5)]
  = [(– 4x2) . 5x + (– 4x2) . 4] + [2x . x2 – 2x . 5]
  = [– 20 x3 – 16x2] + [2 x3 – 10 x]
  = – 20 x3 – 16x2 + 2 x3 – 10 x
  = – 18 x3 – 16x2 – 10 x
   
2x . (– 3x + 7) – 2x2 . (3 + x)
= [2x . (– 3x + 7)] – [2x2 . (3 + x)]
  = [2x . (– 3x) + 2x . 7] – [2x2 . 3 + 2x2 . x]
  = [– 6x2 + 14x] – [6x2 + 2x3]
  = – 6x2 + 14x – 6x2 – 2x3
  = – 12x2 + 14x – 2x3
   
– 3x . (2x2 – 1) – (x2 – 1) . (x + 3)
 = [– 3x . (2x2 – 1)] – [(x2 – 1) . (x + 3)]
  = [(– 3x) . 2x2 – (– 3x) . 1)] – [x2 . x + x2. 3 + (– 1) . x + (– 1) . 3]
  = [– 6x3 + 3x] – [x3+ 3x2 – x – 3]
  = – 6x3 + 3x – x3– 3x2 + x + 3
  = – 7x3 + 4x – 3x2 + 3
 
– (3x – 4) . (x2 – 2) – x2 . (– 3 + x)
= – [(3x – 4) . (x2 – 2)] – [x2 . (– 3 + x)]
  = – [3x . x2 + 3x . (– 2) + (– 4) . x2 + (– 4) . (– 2)] – [x2 . (– 3) + x2 . x]
  = – [3x3 – 6x – 4x2 + 8] – [– 3x2 + x3]
  = – 3x3 + 6x + 4x2 – 8 + 3x2 – x3
  = – 4x3 + 6x + 7x2 – 8
   
– 4 . (x2 – 1) – (2x – 1) . (2x + 1)
 = [– 4 . (x2 – 1)] – [(2x – 1) . (2x + 1)]
  = [(– 4) . x2 – (– 4) . 1)] – [2x . 2x + 2x . 1 + (– 1) . 2x + (– 1) . 1]
  = [– 4 x2 + 4] – [4x2 + 2x – 2x – 1]
  = – 4 x2 + 4 – 4x2 – 2x + 2x + 1
  = – 8 x2 + 5