Activité 8 - Exercices de synthèse

e)
Applique la distributivité et réduis éventuellement les termes semblables.
a3 . (a2 + 3)

= a3 . a2 + a3 . 3

= a5 + 3a3

x2 . (x5 + x3)

= x2 . x5 + x2 . x3

= x7 + x5

3x . (x2 + x3)

= 3x . x2 + 3x . x3

= 3x3 + 3x4

(2x + x2) . (x2 + 1)

= 2x . x2 + 2x . 1 + x2 . x2 + x2 . 1

= 2x3 + 2x + x4 + x2

(x2 + 2) . (3x – x3)

= x2 . 3x + x2 . (– x3) + 2 . 3x + 2 . ( – x3)

= 3x3 – x5 + 6x – 2x3

= –x3 – x5 + 6x

3x . (x – 2x2)

= 3x . x – 3x . 2x2

= 3x2– 6x3

(x – 3) . x2

= x . x2 – 3 . x2

= x3 – 3x2

– 4a . (2a4 – 6a2)

= – 4a . 2a4 – (– 4a) . 6a2

= – 8a5 +24a3

(x3 – 3) . (x2 – 2)

= x3 . x2 + x3 . (– 2) + (– 3) . (x2) + (– 3) . (– 2)

= x5 – 2x3 – 3x2 + 6

(x2 – 2) . (x2 + 1)

= x2. x2 + x2. 1 + (– 2) . x2 + (– 2) . 1

= x4 + x2 – 2x2 – 2

= x4 – x2 – 2