SUP03-19

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Factoriser les expressions suivantes en reconnaissant une identité remarquable.

$A (x) = x^{2} - 9$ ; Corrigé
$\begin{aligned} A (x) & = x^{2} - 9 \\ = x^{2} - 3^{2} \\ = (x - 3) (x + 3) \end{aligned}$
$B (x) = (2 x - 1)^{2} - (x - 1)^{2}$ ; Corrigé
$\begin{aligned} B (x) & = (2 x - 1)^{2} - (x - 1)^{2} \\ = [(2 x - 1) - (x - 1)] [(2 x - 1) + (x - 1)] \\ = (2 x - 1 - x + 1) (2 x - 1 + x - 1) \\ = x (3 x - 2) \end{aligned}$
$C (x) = 1 + 6 x + 9 x^{2}$ ; Corrigé
$\begin{aligned} C (x) & = 1 + 6 x + 9 x^{2} \\ = 1 + 2 \times 1 \times 3 x + (3 x)^{2} \\ = (1 + 3 x)^{2}; \end{aligned}$
$D (x) = x^{4} - 1$ . Corrigé
$\begin{aligned} D (x) & = x^{4} - 1 \\ = (x^{2})^{2} - 1^{2} \\ = (x^{2} - 1) (x^{2} + 1) \\ = (x - 1) (x + 1) (x^{2} + 1) . \end{aligned}$

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code : 253