Exercice 2 :
a)
[tex] {(a + b)}^{3} = (a + b) \times (a + b) \times (a + b) \\ [/tex]
[tex] = ({a}^{2} + 2 \times a \times b + {b}^{2} ) \times (a + b)[/tex]
[tex] = {a}^{3} + a \times (2ab) + a \times {b}^{2} + {a}^{2} \times b + b \times (2ab) + {b}^{3} [/tex]
[tex] = {a}^{3} + 2 {a}^{2} b + {b}^{2} a + {a}^{2} b + 2 {b}^{2} a + {b}^{3} [/tex]
[tex] = {a}^{3} + 3 {a}^{2} b + 3 {b}^{2} a + {b}^{3} [/tex]
b)
[tex] {(a - b)}^{3} = (a - b) \times (a - b) \times (a - b) \\ [/tex]
[tex] = ({a}^{2} - 2ab + {b}^{2} ) \times (a - b)[/tex]
[tex] = {a}^{3} + a \times ( - 2ab) + a \times {b}^{2} - {a}^{2} \times b - b \times ( - 2ab) - {b}^{3} [/tex]
[tex] = {a}^{3} - 2 {a}^{2} b + {b}^{2} a - {a}^{2} b + 2 {b}^{2} a - {b}^{3} [/tex]
[tex] = {a}^{3} - 3 {a}^{2} b + 3 {b}^{2} a - {b}^{3} [/tex]
J'espère t'avoir aidé !
