# Expression algébriques Ex 3

#### Exercice 3

Factoriser chacune des expressions suivantes.

1. $A = x^2 – 6x$
$\quad$
2. $B = 2x^2 + 6x^3$
$\quad$
3. $C = 25x^2 – 16$
$\quad$
4. $D = (2x + 1)^2 – (x – 1)^2$
$\quad$
5. $E = x^2 + 9 + 6x$
$\quad$
6. $F = 4x^2 + 12x + 9$
$\quad$
7. $G = 2x – 5 + (2x – 5)^2$
$\quad$
8. $H = x^2 – 9 + (x – 3)(x + 1)$

#### Correction

1. $A = x^2 – 6x = x \times x – 6 \times x$ $= x(x – 6)$
$\quad$
2. $B = 2x^2 + 6x^3 = 2x^2 \times 1 – 3x \times 2x^2$ $=2x^2(1 – 3x)$
Une version moins bien factorisée est $B = x^2(2 + 6x)$
$\quad$
3. $C = 25x^2 – 16 = (5x)^2 – 4^2$ $=(5x – 4)(5x + 4)$
$\quad$
4. $D = (2x + 1)^2 – (x – 1)^2 = \left[(2x + 1) – (x – 1)\right] \times \left[(2x + 1) + (x – 1)\right]$ $=(x + 2)(3x)$
$\quad$
5. $E = x^2 + 9 + 6x = x^2 + 2 \times 3 \times x + 3^2 = (x + 3)^2$
$\quad$
6. $F = 4x^2 + 12x + 9 = (2x)^2 + 2 \times 2x \times 3 + 3^2 = (2x + 3)^2$
$\quad$
7. $G = 2x – 5 + (2x – 5)^2 = (2x – 5) \times 1 + (2x – 5)^2$ $=(2x – 5)(1 + 2x – 5)$ $=(2x – 5)(2x – 4)$
$\quad$
8. $\quad$
\begin{align} H &= x^2 – 9 + (x – 3)(x + 1) \\\\ = & (x – 3)(x + 3) + (x – 3)(x + 1) \\\\ = & (x – 3)\left[(x + 3) + (x + 1)\right] \\\\ = &(x – 3)(2x + 4) \\\\ =& 2(x – 3)(x + 2) \end{align}