Distributivité ou double distributivité (2)

Souviens toi de ce schéma de développement :

$A = (x + 4)(y + 7)\\A = x \times y + x \times 7 + 4 \times y + 4 \times 7\\A = x y + 7 x + 4 y + 28$

$B = (2 x + 5)(y + 4)\\ B = 2 x \times y + 2 x \times 4 + 5 \times y + 5 \times 4\\ B = 2 x y + 8 x + 5 y + 20$

$C = (3 x + 7)(2 x + 1)\\ C = 3 x \times 2 x + 3 x \times 1 + 7 \times 2 x + 7 \times 1 \\ C = 6 x^2 + 3 x + 14 x + 7 \\ C = 6 x^2 + 17 x + 7$

$D = (x - 3)(y + 7)\\D = x \times y + x \times 7 - 3 \times y - 3 \times 7\\D = x y + 7 x - 3 y - 21$

$E = (x - 5)(x - 4)\\E = x \times x - x \times 4 - 5 \times x + 5 \times 4\\E = x^2 - 4 x - 5 x + 20\\E = x^2 - 9 x + 20$

$F = (2 x - 3)(3 x + 5)\\F = 2 x \times 3 x + 2 x \times 5 - 3 \times 3 x - 3 \times 5\\F = 6 x^2 + 10 x - 9 x - 15\\F = 6 x^2 + x - 15$

$G = (3 x - 7)(2 x - 4)\\G = 3 x \times 2 x - 3 x \times 4 - 7 \times 2 x + 7 \times 4\\G = 6 x^2 - 12 x - 14 x + 28\\G = 6 x^2 - 26 x + 28$

$H = (2 x - 3)(- 5 x + 1)\\H = 2 x \times (- 5 x) + 2 x \times 1 - 3 \times (- 5 x) - 3 \times 1\\H = -10 x^2 + 2 x + 15 x - 3\\H = - 10 x^2 + 17 x - 3$

$I = (5 x - 2)(-3 x - 4)\\I = 5 x \times (- 3 x) + 5 x \times (- 4) - 2 \times (- 3 x) - 2 \times (- 4)\\I = - 15 x^2 - 20 x + 6 x + 8\\I = - 15 x^2 - 14 x + 8$

$J = (-4 x + 2)(2 x + 7)\\J = - 4 x \times 2 x - 4 x \times 7 + 2 \times 2 x + 2 \times 7\\J = - 8 x^2 - 28 x + 4 x + 14\\J = - 8 x^2 - 24 x + 14$

$K = (-3 x + 1)(-5 x + 4)\\K = -3 x \times (-5 x) - 3 x \times 4 + 1 \times (- 5 x) + 1 \times 4\\K = 15 x^2 - 12 x - 5 x + 4\\K = 15 x^2 - 17 x + 4$

$L = (- 2 x - 1)(- 3 x + 7)\\L = - 2 x \times (- 3 x) - 2 x \times 7 - 1 \times (- 3 x) - 1 \times 7\\L = 6 x^2 - 14 x + 3 x - 7\\L = 6 x^2 - 11 x - 7$

$M = (-5 x - 2)(- 4 x - 3) \\M = - 5 x \times (- 4 x) - 5 x \times (- 3) - 2 \times (- 4 x) - 2 \times (- 3)\\M = 20 x^2 + 15 x + 8 x + 6\\M = 20 x^2 + 23 x + 6$

$N = (- 3 x + 7)(- 6 x - 1)\\N = - 3 x \times (- 6 x) - 3 x \times (- 1) + 7 \times (- 6 x) + 7 \times (-1)\\N = 18 x^2 + 3 x - 42 x - 7\\N = 18 x^2 - 39 x - 7$

$O = (- 9 x + 7)(- 6 x + 7)\\O = - 9 x \times (-6 x) - 9 x \times 7 + 7 \times (-6 x) + 7 \times 7\\O = 54 x^2 - 63 x - 42 x + 49\\O = 54 x^2 - 105 x + 49$

$P = (- 7 x - 3)(2 x - 7)\\P = - 7 x \times 2 x - 7 x \times (-7) - 3 \times 2 x - 3 \times (-7)\\P = - 14 x^2 + 49 x - 6 x + 21\\P = - 14 x^2 + 43 x + 21$

$Q = (- 5 x + 1)( 1 - 4 x)\\Q = -5 x \times 1 - 5 x \times (-4 x) + 1 \times 1 + 1 \times (- 4 x)\\Q = -5 x + 20 x^2 + 1 - 4 x\\Q = 20 x^2 - 9 x + 1$

$R = (2 + 3 x)(4 x - 1)\\R = 2 \times 4 x + 2 \times (-1) + 3 x \times 4 x + 3 x \times (-1)\\R = 8 x - 2 + 12 x^2 - 3 x\\R = 12 x^2 + 5 x - 2$

$S = (2 x + 3)(-7 x - 4)\\S = 2 x \times (-7 x) + 2 x \times (-4) + 3 \times (-7 x) + 3 \times (-4)\\S = -14 x^2 - 8 x - 21 x - 12\\S = -14 x^2 - 29 x - 12$

$T = (3 - 5 x)(4 - 7 x)\\T = 3 \times 4 + 3 \times (-7 x) - 5 x \times 4 - 5 x \times (- 7 x)\\T = 12 - 21 x - 20 x + 35 x^2\\T = 35 x^2 - 41 x + 12$