Cours L'incontournable du chapitre

Double distributivité

L'énoncé

Développez les expressions suivantes : 


Question 1

$A = (2x + 5)(5x + 10)$

$A = (2x+5)(5x+10)$

$A = 2x\times5x + 2x\times10 + 5\times5x + 5\times10$

$A = 10x^2 + 20x + 25x + 50$

$A = 10x^2 + 45x + 50$

Question 2

$B = (x-4)(3x-1)$

$B = (x-4)(3x-1)$

$B = x\times 3x – x\times 1 – 4\times 3x + 4\times 1$

$B = 3x² - x – 12x + 4$

$B = 3x² - 13x + 4$

Question 3

$C = (6x+6)(2x-3)$

$C = (6x+6)(2x-3)$

$C = 6x\times 2x – 6x\times 3 + 6\times 2x – 6\times 3$

$C = 12x² - 18x + 12x – 18$

$C = 12x² -6x - 18$

Question 4

$D = (3x+1)(7-x)$

$D = (3x+1)(7-x)$

$D = 3x\times 7 – 3x\times x + 1\times 7 – 1\times x$

$D = 21x – 3x² + 7 – x$

$D = -3x² + 20x + 7$

 

Question 5

$ (11-5x)(3-4x)$

$ (11-5x)(3-4x)$

$E = 11\times 3 – 11\times 4x – 5x\times 3 + 5x\times 4x$

$E = 33 – 44x – 15x + 20x²$

$E = 20x² -59x + 33$

Question 6

$F = (8x – 9)(8x+1)$

$F = (8x – 9)(8x+1)$

$F = 8x\times 8x + 8x\times 1 – 9\times 8x – 9\times 1$

$F = 64x² + 8x – 72x – 9$

$F = 64x² -64x - 9$

 

Question 7

$ G = (5-5x)(2x+7)$

$ G = (5-5x)(2x+7)$

$G = 5\times 2x + 5\times 7 – 5x\times 2x – 5x\times 7$

$G = 10x + 35 – 10x² - 35x$

$G = -10x² - 25x + 35$

Question 8

$H = (x+3)(7-3x)$

$H = (x+3)(7-3x)$

$H = x\times 7 – x\times 3x + 3\times 7 - 3\times 3x$

$H = 7x – 3x² + 21 - 9x$

$H = -3x² -2x + 21$