Soluce

Exercices complémentaires

Série A

6) Applique la distributivité et réduis les termes semblables.

5a – 3 . (2a – 7)	= 5a – [3 . (2a – 7)]
	= 5a – [6a – 21]
	= 5a – 6a + 21
	= – a + 21

(2x – y) + 5 . (x + y)	= (2x – y) + [5 . (x + y)]
	= (2x – y) + [5x + 5y]
	= 2x – y + 5x + 5y
	= 7x + 4y

5 . (a – 3) – 2 . (a + 5)	= [5 . (a – 3)] – [2 . (a + 5)]
	= [5a – 15] – [2a + 10]
	= 5a – 15 – 2a – 10
	= 3a – 25

– 2 . (a – 3b) – 4 . (2b + 1)	= [– 2 . (a – 3b)] – [4 . (2b + 1)]
	= [– 2a + 6b] – [8b + 4]
	= – 2a + 6b – 8b – 4
	= – 2a – 2b – 4

5a . (a – 3) – 2 . (a + 5)	= [5a . (a – 3)] – [2 . (a + 5)]
	= [5a² – 15a] – [2a + 10]
	= 5a² – 15a – 2a – 10
	= 5a² – 17a – 10

3a – (2a + 3) . (5 – 2a)	= 3a – [(2a + 3) . (5 – 2a)]
	= 3a – [10a – 4a² + 15 – 6a]
	= 3a – 10a + 4a² – 15 + 6a
	= 4a² – a – 15

(2 + a) . (3 – a) + (5 – a) . (– a + 2)	= [(2 + a) . (3 – a)] + [(5 – a) . (– a + 2)]
	= [6 – 2a + 3a – a²] + [– 5a + 10 + a² – 2a ]
	= 6 – 2a + 3a – a² – 5a + 10 + a² – 2a
	= – 6a + 16

(x + 2) . (2x – 1) – (3x – 2) . (x – 4)	= [(x + 2) . (2x – 1)] – [(3x – 2) . (x – 4)]
	= [2x² – x + 4x – 2] – [3x² – 12x – 2x + 8
	= 2x² – x + 4x – 2 – 3x² + 12x + 2x – 8
	= – x² + 17x – 10


5x + (x + 3) . (3x – 1) – (2x – 1) . (– x + 2)	= 5x + [(x + 3) . (3x – 1)] – [(2x – 1) . (– x + 2)]
	= 5x + [3x² – x + 9x – 3] – [– 2x² + 4x + x – 2]
	= 5x + 3x² – x + 9x – 3 + 2x² – 4x – x + 2
	= 5x² + 8x – 1


– (5x – 1) . (x + 1) + (– x – 1) . (– x + 2)	= – [(5x – 1) . (x + 1)] + [(– x – 1) . (– x + 2)]
	= – [5x² + 5x – x – 1] + [ x² – 2x + x – 2]
	= – 5x² – 5x + x + 1 + x² – 2x + x – 2
	= – 4x² – 5x – 1