☺ Salut ☺
✅EXO1
Soit x un réel quelconque, développons chacune des expressions :
[tex]A(x) = {(3x + 6)}^{2}[/tex]
[tex]\boxed{\boxed{A(x) = 9{x}^{2} + 36x + 36}}[/tex]✔
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[tex]B(x) = (x\sqrt{2} - 1)(x\sqrt{2} + 1)[/tex]
[tex]B(x) = {(x\sqrt{2})}^{2} - {(1)}^{2}[/tex]
[tex]B(x) = {(x)}^{2} \times {(\sqrt{2})}^{2} - {(1)}^{2}[/tex]
[tex]B(x) = {x}^{2}\times2 - {(1)}^{2}[/tex]
[tex]\boxed{\boxed{B(x) = 2{x}^{2} - 1}}[/tex]✔
✅EXO2
Soit x un réel quelconque, factorisons chacune des expressions :
[tex]C(x) = {(x - 4)}^{2} - {(2x + 5)}^{2}[/tex]
[tex]C(x) = [(x - 4) + (2x + 5)][(x - 4) - (2x + 5)][/tex]
[tex]C(x) = (x - 4 + 2x + 5)(x - 4 - 2x - 5)[/tex]
[tex]\boxed{\boxed{C(x) = (3x + 1)(- x - 9)}}[/tex]✔
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[tex]D(x) = 9{x}^{2} - 12x + 4[/tex]
[tex]\boxed{\boxed{D(x) = {(3x - 2)}^{2}}}[/tex]✔
✅EXO3
Pour factoriser [tex]{(x + 8)}^{2} - 9[/tex]
On utilise :
a. [tex]\:{a}^{2} + 2ab + {b}^{2} = {(a + b)}^{2}[/tex]
b. [tex]\:{a}^{2} - 2ab + {b}^{2} = {(a - b)}^{2}[/tex]
c. [tex]\boxed{\boxed{{a}^{2} - {b}^{2} = (a + b)(a - b)}}[/tex]✔
