Réponses

2013-12-13T19:44:18+01:00
Exercice - 1 :

A = -3 +  \frac{-3}{10} * \frac{-10}{3} = -3 + 1 = -2

B =  \frac{-5}{6} * ( \frac{-11}{10} - \frac{-1}{11} ) =  \frac{-5}{6}  *(- \frac{111}{110}) =  \frac{37}{44}

C =  \frac{ \frac{5}{3} - 6 }{ \frac{-5}{4} + 8 } =  \frac{- \frac{13}{3} }{ 6,75 } = - \frac{52}{81}

Exercice - 2 :

A =  \frac{500* 10^{-6}*140*  10^{-6}  }{400*( 10^{2})^{4}  } =  \frac{1* 10^{-12} *70000}{4* 10^{10} } =  \frac{7 *  10^{-8} }{4*10^{-10} } = 175 = 1,75 * 10^{2}

B =  \frac{280*10^{8}*140*10^1 }{1120*(10^{-2})^{5}  } =  \frac{39200*1000000000}{1,12 *  10^{-7} } = 3,5 *  10^{20}

Exercice - 3 :

A = ( 2x - 4 )^2
= (2x)^2 - 2 * 2x * 4 + 4^2
= 4x^2 - 16x + 16

B = ( 6x + 2 )^2
= (6x)^2 + 2 * 6x * 2 + 2^2
= 36x^2 + 24x + 4

C = ( 3x + 9 ) ( -x + 5 )
= 3x * (-x) + 3x * 5 + 9 * (-x) + 9 * 5
= -3x^2 + 15x - 9x + 45
= -3x^2 + 6x + 45

D = ( 8x + 7 ) ( 8x - 7 )
= (8x)^2 - 7^2
= 64x^2 - 49

E = ( 8x - 6 ) ( 8x + 6 ) - ( 7x - 7 )^2
= (8x)^2 - 6^2 - (7x)^2 - 2 * 7x * 7 + 7^2
= 64x^2 - 36 - 49x^2 - 98x + 49
= 15x^2 - 98x + 13

F = - ( 7x + 9 )^2 + ( -4x + 5 ) ( -4x - 9 )
= - (7x)^2 + 2 * 7x * 9 + 9^2 - 4x * (-4x) - 4 * (-9) + 5 * (-4x) + 5 * (-9)
= -49x^2 + 126x + 81 + 16x^2 + 36 - 20x - 45
= -23x^2 + 106x + 72