Réponse:

Les identités remarquables :

[tex] ({x + y})^{2} = {x}^{2} + 2xy + {y}^{2} [/tex]

[tex]( {x - y})^{2} = {x}^{2} - 2xy + {y}^{2} [/tex]

[tex](x + y)(x - y) = {x}^{2} - {y}^{2} [/tex]

Exercice 4:

a)

Il faut utiliser la 2eme règle (x-y)^2

[tex] ({2 - 7x})^{2} = {2}^{2} - 2 \times 2 \times 7x + ({7x})^{2} = 4 - 28x + 49 {x}^{2} [/tex]

b)

[tex]( {3x + \frac{1}{3} })^{2} = 9 {x}^{2} + 2x + \frac{1}{9} [/tex]

c)

[tex](4x - \frac{2}{5} )(4x + \frac{2}{5} ) = 16 {x}^{2} - \frac{4}{25} [/tex]

d)

[tex]( { - 2a + 4.5})^{2} = ( { - 2a + \frac{9}{2} })^{2} = 4 {a}^{2} + 2 \times ( - 2a) \times \frac{9}{2} + \frac{81}{4} = 4 {a}^{2} - 18a + \frac{81}{4} [/tex]