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résolu

Développer et réduire les expressions suivantes:

A=(7x+3)²    B=8x-4)²    C=(6x-5)(6x+5)    D=(9x-4)(11x-2)

G=(5x+11)(4x-7)-(5x+11)²

Répondre :

A = ((7x)² + 2×7x×3 + 3²)
   = (49x² + 42x + 9)
   = 49x² + 42x + 9

B = (8x - 4)²
   = ((8x)² - 2 × 8x × 4 + 4²)
   = 64x² - 64x + 16

C = (6x-5)(6x+5)
   = ((6x)² - 5²)
   = 36x² - 25

D = (9x-4)(11x-2)
   = (99x² - 18x - 44x + 8)
   = 99x² - 62x + 8

G = (5x+11)(4x-7)-(5x+11)²
   = (20x² - 35x + 44x - 77) - ((5x)² + 2 × 5x × 11 + 11²)
   = (20x² + 9x - 77) - (25x² + 110x + 121)
   = 20x² + 9x - 77 - 25x² - 110x - 121
   = - 5x² - 101x - 198
A = ( 7x + 3 )² 
= (7x)^2 + 2 * 7 * 3 + 3^2
= 49x^2 + 42 + 9
= 49x^2 + 51

B = ( 8x - 4 )²
= (8x)^2 - 2 * 8x * 4 + 4^2
= 64x^2 - 64 + 16
= 64x^2 - 48

C = ( 6x - 5 ) ( 6x + 5 ) 
= (6x)^2 - 5^2
= 36x^2 - 25

D = ( 9x - 4 ) ( 11x - 2 )
= 9x * 11x + 9x * (-2) - 4 * 11x - 4 * (-2)
= 99x^2 - 18x - 44x + 8
= 99x^2 - 62x + 8

G = ( 5x + 11 ) ( 4x - 7 ) - ( 5x + 11 )²
= 5x * 4x + 5x * (-7) + 11 * 4x + 11 * (-7) - [ (5x)^2 + 2 * 5x * 11 + 11^2 ]
= 20x^2 - 35x + 44x - 77 - 25x^2 - 110x - 121 ]
= -5x^2 + 101x + 198

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