Expression algébrique Ex 4

Exercice 4

Factoriser

  1. $A = (2x + 1)^2 – (3x – 4)^2$
    $\quad$
  2. $B = (3x – 2)^2 – (x + 1)^2$
    $\quad$
  3. $C = \left(x + \sqrt{2}\right)^2 – \left(3x + \sqrt{3}\right)^2$
    $\quad$
  4. $D = \left(-x + \sqrt{5}\right)^2 – \left(2x – \sqrt{5}\right)^2$

Correction

  1. $A = (2x + 1)^2 – (3x – 4)^2 = \left[(2x + 1) – (3x – 4)^2\right] \times \left[(2x + 1) + (3x – 4)^2\right] $ $=(-x + 5)(5x – 3)$
    $\quad$
  2. $B = (3x – 2)^2 – (x + 1)^2 = \left[(3x-2)-(x + 1)\right] \times \left[(3x-2) + (x + 1)\right] $ $=(2x-3)(4x-1)$
    $\quad$
  3. $\quad$
    $\begin{align} C &= \left(x + \sqrt{2}\right)^2 – \left(3x + \sqrt{3}\right)^2 \\\\
    =& \left[\left(x + \sqrt{2}\right) – \left(3x + \sqrt{3}\right)\right] \times \left[\left(x + \sqrt{2}\right) + \left(3x + \sqrt{3}\right)\right] \\\\
    =&\left(-2x + \sqrt{2} – \sqrt{3}\right) \left(4x + \sqrt{2} + \sqrt{3}\right)
    \end{align}$
  4. $\quad$
    $\begin{align} D & = \left(-x + \sqrt{5}\right)^2 – \left(2x – \sqrt{5}\right)^2 \\\\
    =& \left[\left(-x + \sqrt{5}\right) – \left(2x – \sqrt{5}\right)\right] \times \left[\left(-x + \sqrt{5}\right) + \left(2x – \sqrt{5}\right)\right] \\\\
    = & x\left(-3x + 2\sqrt{5}\right)
    \end{align}$