Calcul littéral 1 – 2 – 3 : DM 5 ème

Détaillez vos calculs.

I) Supprimer les signes × et réduire (si possible) :
A = 5 × x × y
B = 3 × 6 × x
C = 6 + 10 × x
D = 7 × x × y × 2
E = 3 × x × x
F = 3 × x + 5 × y
G = 6 × x − 3 × y
H = 8 × x × 3 × y
I = a × 4 + 6 × b
J = 5 × x × x × 3
K = [(a ×4) + (b 2)]
L = 3 × a × b × a – c × 4 × a
M = 2 × (3 × x × 2 × y)
N = 8 × a + 15 × a – 3 × a
O = 19 x – 13 x + 11 x
P = 4 × b × 9 + 4 × a × a − c × 3
Q = 2 × a × a + b × b × b


II) Développer puis réduire :
A = 4 (x – 3)
B = 5 (3 x − 6)
C = 3 (4 x – 3)
D = 6 (2 x + 9)
E = 2 (4 x + 4 y − 3)
F = 3 x (2 x − 7)
G = 4 (2 x + 5) + 3 (x − 6)
H = 2 (3 x + 4 y – 2)
I = 2 x (x + 1) + x (5 x − 2)
J = 2 (3 x + 5) + 4 (2 x + 3)
K = 3 (2 x + 5) + 2 (4 x + 3)
L = 4 (2 x + 7) + 3 (x − 6)
M = 5 (3 x + 4) + 6 (2 x − 3)
N = (x – y) × x
O = 2 (4 a + 2 b) + 3 (6 a – b) + a (2 + b)
P = 4 (2 x + 3 y + 4) + 3 (5 x + 2 y − 5)
Q = 3 x (5 x + 3) + 6 x² + 2

III) Factoriser :
A = 6 a – 3
B = 4 – 4 x
C = 9 a + 5 a2
D = a × b – 13 a
E = 2 a × 3 x + 4 × 2 a
F = 4 a2 – a b
G = x × 3 b + x × c
H = 3 a b + 3 a c
I = 6 a b + 2 a c
J = 2 a + 7 a × 2 b – 3 a2 × 2


IV) Calculer de deux façons différentes :
A = 3 × 5 + 3 × 2
B = 6 × 2 − 5 × 2
C = 4 (5 − 3)
D = 4 × 5 + 4


V) Calculer astucieusement :
A = 45 × 99
B = 2,7 × 3,6 + 2,7 × 6,4
C = 18 × 101
D = 57 × 0,82 + 0,82 × 43
E = 34 × 45 + 64 × 45 – 45 × 8
F = 12 × 9,9
G = 7,53 × 3,26 + 6,74 × 7,53
H = 456,7 × 1001
I = 12 × 199
J = 21 × 65,7 + 9 × 65,7 + 30 × 34,3
K = 265 × 102