Expressions algébriques Ex2

Exercice 2

Développer et réduire les expressions algébriques.

  1. $A = (x – 1)^2 – (2x + 3)^2$
    $\quad$
  2. $B = x^2 – (x – 5)^2$
    $\quad$
  3. $C = (3x – 1)^2 + (3 + x)^2$
    $\quad$
  4. $D = (4x + 1)(x – 2)$
    $\quad$
  5. $E = (x – 2)(x + 1) (x – 3)$

Correction

  1. $A = (x – 1)^2 – (2x + 3)^2 = x^2 – 2x + 1 – (4x^2 + 12x + 9) $ $= x^2 -4x + 1 – 4x^2 – 12x – 9$ $=-3x^2 – 14x – 8$
    $\quad$
  2. $B = x^2 – (x – 5)^2 = x^2 – (x^2 – 10x + 25) $ $=x^2 – x^2 + 10x – 25$ $=10x – 25$
    $\quad$
  3. $C = (3x – 1)^2 + (3 + x)^2 = 9x^2 – 6x + 1 + 9 + 6x + x^2 $ $=10x^2 + 10$
    $\quad$
  4. $D = (4x + 1)(x – 2) = 4x^2 – 8x + x – 2 $ $=4x^2 – 7x – 2$
    $\quad$
  5. $E = (x – 2)(x + 1)(x – 3) = (x – 2)(x^2 – 3x + x – 3) $ $=(x – 2)(x^2 – 2x – 3)$ $=x^3 – 2x^2 – 3x – 2x^2 + 4x + 6 $ $=x^3 – 4x^2 + x + 6$