Corrigé des exercices sur factoriser et développer en 2de.

EXERCICE 1 :

$a) 3x(x+5) = 3x^2 + 15x\\ b) -2x(x+6) = -2x^2 - 12x\\ c) -3x(4-5x) = -12x + 15x^2\\ d) (1+x)(1+2x) = 1 + 3x + 2x^2\\ e) (x^2+2)(x-1) = x^3 - x^2 + 2x - 2\\ f) 2x^2(1-3x^2) = 2x^2 - 6x^4$

EXERCICE 2 :

$a) (x+3)(x+5)-4x \\= x^2 + 8x + 15\\\\ b) x(3-2x)+5x^2+2x \\= -2x^2 + 8x^2 + 2x\\\\ c) (5-t)(1+2t)+2(3t+4) \\= -2t^2 + t + 22\\\\ d) 2x^2(x+6)-x^3+4x^2-2x \\= x^3 + 6x^2 - 2x\\$

EXERCICE 3 :

$a) (x+12)^2 = x^2 + 24x + 144\\\\ b) (3x+1)(3x-1) = 9x^2 - 1\\\\ c) (6-x)^2 = x^2 - 12x + 36\\\\ d) (x+1)^2+(x-2)^2 \\= 2x^2 - 2x + 5\\$

EXERCICE 4 :

$a) (x+10)^2 = x^2 + 20x + 100\\\\ b) (x+9)(x-9) = x^2 - 81\\\\ c) x^2 + 16x + 64 = (x+8)^2$

EXERCICE 5 :

$a) (x+\frac{1}{2})^2 = x^2 + x + \frac{1}{4}\\\\ b) (3x-\frac{1}{3})^2 = 9x^2 - 2x + \frac{1}{9}\\\\ c) (x+\frac{2}{5})(x-\frac{2}{5}) = x^2 - \frac{4}{25}\\\\ d) (a+\sqrt{5})^2 = a^2 + 2a\sqrt{5} + 5\\\\$

EXERCICE 6 :

$a) 3(x-5)\\\\ b) x(4x-7)\\\\ c) x(3x-4)(x+2)\\\\ d) 3a(a-2)\\\\ e) 3x^2(x+3)\\\\ f) (\sqrt{x}+2)(\sqrt{x})$

EXERCICE 7 :

$a) (2x-3)(2x-3)(11x+2)\\\\ b) (15x+7)(15x+7)-(x-3)(12x+5)\\\\ c) (7x-26)(12x+4)(11x+28)\\\\ d) (13t+5)(-8t+15)\\\\$

EXERCICE 8 :

$a) (x+2\sqrt{3})(x-2\sqrt{3})\\\\ b) (3y+2)^2\\\\ c) (x-13)^2\\\\ d) 36(x+1)^2\\\\ e) (5x+3)(x+1)\\\\ f) (3t-2)^2\\\\ g) (11x-1)(11x-1)\\\\ h) (x-2)(x+2)$

EXERCICE 9 :

$A = (x-1)(x-2)\\\\ B = -(3x+1)(3x-1)\\\\ C = (x-4)^2\\\\ D = (2x-1)(-x+1)\\\\ E = (x+1)^2+1\\\\ F = (x+\sqrt{2})(x-\sqrt{2})\\\\ G = 4(x-1)^2\\\\ H = -26x^2+30x-9\\\\ I = (x^2-1)(x+1)^2\\\\ J = 3(x-5)(x-1)\\\\ K = (x-11)^2-5(x+3)^2\\\\ L = (2x-3)(-2x+9)\\\\ M = x^3+3x^2+2x\\\\ N = 0,3(x-1,5)^2\\\\ O = 0,25(x-2)^2+1\\\\ P = -2x-1\\\\ Q = -40(x-1)^2\\\\ R = (x-1)^2\\\\ T = 50x^2-28x+72\\\\ U = -6(x-7)(3x-5)\\\\ V = (x-4)(x+1)\\\\ W = (x+1)(x+5)\\\\ X = (x+1)(3x+2)\\\\ Y = (x-\frac{1}{2})(-4x-2)\\\\ Z = (x-1)(2x-1)\\\\ A' = x(x+1)^2$