تصحيح
تمرين1
A = ( 4x + √13 ) ( 4x - √13 ) - ( 6x + 5 )
= ( 4x )2 - ( √13 )2 - [ ( 6x)2 - 2X 6x X 5 + 52 ]
= 16x 2 - 13 - [36x2 - 60x +25 ]
= 16x 2 - 13 - 36x2 + 60x -25
= 16x 2 - 36x2 + 60x -25 - 13
= -20x 2 + 60x - 38
B = ( 2x - 3 )2 - ( 2x - 1 ) ( 4x + 3 )
= [( 2x)2-2 X2x X 3 + 32 ] - ( 2x X 4x +2x X 3 - 1 X 4x - 1 X 3 )
= 4x2-12x + 9 - ( 8x2 +6x - 4x - 3 )
= 4x2-12x + 9 - 8x2 - 2x + 3
= 4x2 - 8x2 - 2x -12x + 3 + 9
= - 4x2 -14x +12
تمرين2
C = 81 x4 - 16
=( 9x2)2 - 42
=( 9x2 - 4 )( 9x2 +4 )
D = 25 x2 - 70 x + 49 + ( 6x - 1 ) ( 7 - 5x )
= (5 x)2 - 2 X 5X 7x + 72 + ( 6x - 1 ) ( 7 - 5x )
= (5 x - 7)2 + ( 6x - 1 ) ( 7 - 5x )
= (5 x - 7)2 +[ -( 6x - 1 ) ( 5x - 7)]
= (5 x - 7)2 -( 6x - 1 ) ( 5x - 7)
= (5 x - 7)[ ( 5x - 7) -( 6x - 1 ) ]
= (5 x - 7) ( 5x - 7 - 6x + 1 )
= (5 x - 7) ( - x -6 )
E = ( 3x + 4 )2 - 2 ( 6x2 + 8x ) + 4x2
= ( 3x + 4 )2 - 2 X[ 2x ( 3x + 4 ) ] + 4x2
= ( 3x + 4 )2 - 2 X2x ( 3x + 4 ) + 4x2
= ( 3x + 4 )2 - 2 X2x ( 3x + 4 ) + (2x)2
= ( 3x + 4 -2x )2
= ( x + 4 )2
تمرين 3
F = [ ( a-1 b2 ) -3a4b-2 ] / (a2b-1 ) 5
=[ ( a-1)-3( b2 ) -3a4b-2 ] / (a2 )5 (b-1 ) 5
= [ a3 b -6a4b-2 ] / a10 b- 5
= a3+4-10 b-6-2+5
= a-3 b-3
= (ab)-3
أحسب هذا العدد إذا علمت أن
a = 10 -3 و b = 122
F = (10-3 10 2 ) -3
= (10-1 ) -3
= 103 = 1000
تمرين 4
G = 56 x 25 + 28
= 7X8 X 25 + 28
= 7X23 X 25 + 28
= 7X23 +5 + 28
= 7X28 + 28
= 28 (7 + 1)
= 28 x8
= 28x23
= 211
H = 5-2 + [ 5-2 + ( 25 / 24) -1 ] -7
= 1/25 + [ 1/25 + 24/25 ] -7
= 1/25 + [25 /25 ] -7
= 1/25 + [1 ] -7
= 1/25 + 1
= 1/25 + 25/25
= 26/25
تمرين 5
96000 x 10-20
I = ________________
0,00000025
9,6x104 x 10-20
I = ________________
2,5 x 10-7
9,6x104 x 10-20
I = ________________
2,5 x 10-7
I = (9,6/ 2,5)) x104 x10-20x107
= (96/ 25)) x 104x 10-20x107
= 3,44 x 10-11
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