Exercice - 1 :
[tex]A = -3 + \frac{-3}{10} * \frac{-10}{3} = -3 + 1 = -2[/tex]
[tex]B = \frac{-5}{6} * ( \frac{-11}{10} - \frac{-1}{11} ) = \frac{-5}{6} *(- \frac{111}{110}) = \frac{37}{44} [/tex]
[tex]C = \frac{ \frac{5}{3} - 6 }{ \frac{-5}{4} + 8 } = \frac{- \frac{13}{3} }{ 6,75 } = - \frac{52}{81} [/tex]
Exercice - 2 :
[tex]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} [/tex]
[tex]B = \frac{280*10^{8}*140*10^1 }{1120*(10^{-2})^{5} } = \frac{39200*1000000000}{1,12 * 10^{-7} } = 3,5 * 10^{20} [/tex]
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
