Bonjour pouvez m’aider sur un exercice de math (calcule littéral) sur la distributivité : développer - factoriser Merci d’avance

Bonjour ! ;)

Réponse :

Exercice 13 :

A = 5 - 4x (x - 6)

A = 5 - 4x * x - 4x * (- 6)

A = 5 - 4x² + 24x

⇔ A = - 4x² + 24x + 5

B = (8x + 1) (7x - 3)

B = 8x * 7x + 8x * (- 3) + 1 * 7x + 1 * (- 3)

B = 56x² - 24x + 7x - 3

B = 56x² - 17x - 3

C = (9x - 2) (- 3x + 12)

C = 9x * (- 3x) + 9x * 12 - 2 * (- 3x) - 2 * 12

C = - 27x² + 108x + 6x - 24

C = - 27x² + 114x - 24

D = (4x - 3)²

D = (4x - 3) (4x - 3)

D = 4x * 4x + 4x * (- 3) - 3 * 4x - 3 * (- 3)

D = 16x² - 12x - 12x + 9

D = 16x² - 24x + 9

Exercice 14 :

A = 12x² - 8x

A = 3 * 4 * x * x - 2 * 4 * x

A = 4x (3x - 2)

B = (x - 2)² + 3 (x - 2)

B = (x - 2) (x - 2) + 3 (x - 2)

B = (x - 2) * [ (x - 2) + 3 ]

B = (x - 2) (x + 1)

C = 16x² - 49

C = (4x)² - 7²

( rappel : a² - b² peut se factoriser sous la forme (a - b) (a + b) ! )

C = (4x - 7) (4x + 7)

Bonjour ,

A = 5 - 4x (x - 6) = 5 - 4x × x - 4x × (- 6)

= 5 - 4x² + 24x

On réécrit

= - 4x² + 24x + 5

B = (8x + 1) (7x - 3) = 8x × 7x + 8x ×- 3 + 1 7x + 1 ×- 3 = 56x² - 24x + 7x - 3 = 56x² - 17x - 3

C = (9x - 2) (- 3x + 12)

= 9x × (- 3x) + 9x × 12 - 2 × (- 3x) - 2 × 12

= - 27x² + 108x + 6x - 24 = - 27x² + 114x - 24

D = (4x - 3)²

= 4x × 4x - 4x × ( 3) ×2 + 3 × 3

= 16x² - 24x + 9

Exercice 14 :

A = 12x² - 8x

= 3x× 4x - 2× 4 x

= 4x (3x - 2)

B = (x - 2)² + 3 (x - 2)

= (x - 2) (x - 2) + 3 (x - 2)

= (x - 2) [ (x - 2) + 3 ] = (x - 2) (x + 1)

C = 16x² - 49 = (4x)² - 7²

= (4x - 7) (4x + 7)