Calculs élémentaires

CALCULS
I) Fractions :
4 2 1
−3
A = −
5 5 3
2 7
1
B = − ×
a 5 a a
−
4 2
3
−1
3
2
5
×
C =
1,5+ 1 18
2
1 1
+
2a a
D = a −2+
5
4
7 a
−
2
6 3 a
×
E =
4a 7
1−
14
2
2+ 3 5
÷
F =
2+ 7 3
2
7 2 5
× − −1 + 1
G =
18 7 3
2
2 3
5 8
− ÷ −
H =
5 4
8 3
a a 7
7
I = − × −
3 3 21 21
3 2 4 3
−
−
4 3 5 4
÷
J =
3 2 4 3
+
+
4 3 5 4
a a
a+ −
3 2
K =
3a a
2a+
+
4 3
−5+ 3 2×2+ 4
L =
12×2+ 10
1
1−
2
a
+
M =
a+ 1
1
1+
a
( )
(
)
()
( )
( )
1.1
II) Puissances :
49×(−2)5×(−3)− 2
A =
−73×16×3−3
(−5)4×7 2×(−2)−3
B =
(−4)4 ×(−1)5 ×25
−3
(
)
(a 2 b 4 )2
3
a
D = 0,0000000005×1004000000
23 2 2
E = 4÷ 5
3 3
(a 2 b)3
F =
(−a)(−b)2
C =
G =
H =
I
=
J
=
K =
L =
M =
N =
O =
P =
Q =
R =
(
(
4−2 ×8 4
907×30−2
3
)
√ √
E =
F =
G =
H =
2
)
5 5×24−3
(100−7×156)4
2 2×10−10×2 7×10−6
32×10−15
3 −2 −2
(3 a 2 b 3)3
a b
×
a 4 b −3
(2−1 ab)2
3
8
5 ×3 ×5 2
125×5 2×81×70
0,9×7×10−1×250
14×103 ×0,5×10−2
(568×81−2× 257 )3
(505 ×700 3)4
0,04×2−2 ×(10− 2)3 ×10 2
3×10−8×10−2
25×(102 )−5 ×121
11×75×10−9
9n+ 1+ 9 n
(n ∈ ℕ)
32n+ 1−3 2n
(ab 2)2 (ab−1)3 (a 2 b)− 2
a 2 c−5 (a −1 bc 2)3
(ab−2 c 3 )4 (a 4 b 5 c−6 )− 2
(a −7 b 8 c 7 )3 (a 6 b5 c 4)2
( )
III) Racines :
A = √ 2+ 3 √ 8−6 √ 50
1
1
B = √ 2+
−
2
8
3
√
C =
√ 3−2
2 21 75 a 2
D = √ √
√ 35 √ 20
I
=
J
=
K =
L =
M =
N =
O =
P =
Q =
R =
(
√ 10−2 √5
2
2
)( )
+
1+ √ 5
4
4
3
(√ 2+ √ 7)
2
2
2
(2 a+ √ b) + (1−2 a √ b) −(2 a √ b)
√3
2
√3 –
2
√3 –
√3
3 √ 5+ √ 20
5 4
√ 45 2− 6 + 3 (1− √ 3)
2
(4+ 3 √ 2) −(2+ √ 2)(√ 2−1)
7+ 4 √ 3
7−4 √ 3
+
7− 4 √ 3
7+ 4 √ 3
√ 3+ √ 2 + √ 3− √ 2
√ 3− √ 2 √ 3+ √ 2
√ 0,04 + √ 0,01
√ 0,0016 √ 0,04
2
(√ 2− √ 2+ √ 2+ √ 2)
a 6 + a 6+ a 6 + a 6
5 2+ 5 2+ 52 + 5 2
(
√
)
√
√
√√√
√ √
6− 6− 6− 6−
√
√√
48 a 6 b12
243(ab)4
4 √ 27
3 √3
4 80+ 5×853
28×2 155
2
S = ( 1+ √ 1−a 2+ √ 1−√ 1−a 2 )
(a ∈ [0 ; 1])
IV) Factorisations :
A = x 2 – 9 – (2 x – 6) x+ ( x – 3)2
B = (x – 11)2+ (33 – 3 x)( x+ 2)
C = (x 4 – 1)(x 2+ 2 x+ 1)
D = – 0,3(2 x – 3)2 + 0,7 x (1,5 – x)
E = 0,25 x 2 – x+ 1
F = x 2 – 3 x+ 2
G = – 9 x2– 6 x – 1
H = – 10+ ( x+ 5)2 – 2 x
I = – 2 x 2+ x+ 1
J = x 2+ 2 √ 2 x+ 2
K = x2– 2
L = 4 x 2 – 12 x+ 8
M = x –(3 x – 1)3+ 2 x –1
1
3
x–
N = (2 x – 1) x+ (1– 2 x)2+ x –
2
2
1
O = x 2 1+ + 2( x+ 1)2
x
P = x 2 – (x+ 1)2
Q = 5(1 – x)2 – 45 x 2
R = (x+ 1)2 – 2( x+ 1)+ 1
S = x 5 + 4 x 4+ 4 x 3
T = (5 x – 1)( x+ 3)+ 3(25 x 2 – 1)
U = 49 – 28 x+ 4 x 2 + (7 – 2 x)(5 – 3 x)
V = x 2 (x – 4)+ 2 x ( x – 4)+ x – 4
W = x 2+ 6 x+ 5
X = 3 x 2+ 7 x+ 2
Y = – 2 x 2 – x+ 1
Z = 2 x 2 – 3 x+ 1
( )( )
( )