Chapitre 5

Calcul littéral

Activité 2 - Calcul algébrique : applications

a)	Réduis les expressions suivantes.

x . 4x =	...................	4.(3a + 2a) =	...................	4a + 4a =	...................
2a . 3a =	...................	2.(x + 3x) =	...................	4a . 4a =	...................
4a + 6a =	...................	4x . x . 2x =	...................	x² . 4x =	...................
x² . 2x =	...................	2x + 2 . 3x =	...................	4x² + x² =	...................
a² + a² =	...................	3x . x + x² =	...................	4x . 4 =	...................

b)	Applique la distributivité simple.

2 . (a + b) =	...................	a . (a + b) =	...................
a . (2b + c) =	...................	2a . (b + 3a) =	...................
3a . (2b + 4c) =	...................	x . (x + 2y) =	...................
2 . (b + 1) =	...................	b . (c + 3b) =	...................
3 . (a + 5) =	...................	6a . (a + 2b) =	...................

c)	Applique la double distributivité et additionne les éventuels termes semblables.

(a + b) . (c + d) =	...............................................................................................
(2a + 3c) . (b + 4d) =	...............................................................................................
(a + 3) . (a + 4) =	...............................................................................................
(2b + 4) . (3 + b) =	...............................................................................................
(x + 2) . (x + 3) =	...............................................................................................

d)	Mets le ou les facteurs communs en évidence.

3a + 3b =	...................	9a + 6b =	...................
ac + ab =	...................	12x + 8y =	...................
5ab + 5ac =	...................	18x + 15z =	...................
3ax + 5ay =	...................	32xy + 24xz =	...................
2a + 2 =	...................	6ab + 2ac =	...................
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a² + ab =	...................	8a + 40 ab =	...................
b² + 3ab =	...................	15a² + 10a =	...................
3a² + 7a =	...................	9x + 9x² =	...................
4b² + 5ab =	...................	14c + 7c² =	...................
5a² + 5a =	...................	25d² + 35d =	...................

e)	Réduis les sommes suivantes

3a + 5a =	...................	2a² + 3a² =	...................	a – a =	...................
7b – 3b =	...................	2a² – 5a² =	...................	3a – a =	...................
2a – 5a =	...................	a² – 4a² =	...................	a³ – 2a³ =	...................
–x – 3x =	...................	–x² + 3x² =	...................	4a² – a² =	...................
–a + 7a =	...................	4a³ - a³ =	...................	–a² – a² =	...................

f)	Réduis les expressions qui peuvent l'être.

2a . (–3b) =	...................	5x² – 3x² =	...................	3b – b² =	...................
–4a . (–2a) =	...................	4x³ – x³ =	...................	3b² – b² =	...................
–4a – 2a =	...................	–2x² – 3x² =	...................	3b . (–b²) =	...................
2a – 3b =	...................	x² – x =	...................	–3b – b =	...................
–2a + 3a =	...................	–x . x² =	...................	–b³ + 2b³ =	...................

Vos remarques sont les bienvenues.