bonjour pouvez vous m’aider svp calcul littéral: 1) développer : ( x-6)au carré -(x-6)(2x-5) 2) factoriser au maximum : (x-6) au carré -(x-6)(2x-5) 3) factorise

Bonjour,

1)

(x-6)² - (x-6) ( 2x-5) = x² - 12x + 36 -( 2x² - 5x - 12x + 30)

= x² - 12x + 36 - 2x² + 5x + 12x - 30

= -x² + 5x + 6

2)

(x-6)² - (x-6) ( 2x-5) = (x-6) (x - 6 - 2x + 5)

= (x-6) (-x -1)

= (6-x) (x+1)

3)a)

9t² - 27t = 9t * t + 3 * 9t = 9t (t+3)

b)

-3z + 15 = 15 - 3z = 3*5 - 3z = 3( 5-z)

Bonjour,

1. Développer :

A = (x - 6)² - (x - 6)(2x - 5)

>> identité remarquable :

• (a - b)² = a² - 2ab + b²

A = x² - 12x + 36 - (x - 6)(2x - 5)

>> double distributivité :

• (a + b)(c + d) = ac + ad + bc + bd

A = x² - 12x + 36 - (2x² - 5x - 12x + 30)

A = x² - 12x + 36 - (2x² - 17x + 30)

A = x² - 12x + 36 - 2x² + 17x - 30

A = -x² + 5x + 6

✅

2. Factoriser au maximum :

A = (x - 6)² - (x - 6)(2x - 5)

A = (x - 6)(x - 6) - (x - 6)(2x - 5)

A = (x - 6)(x - 6 - (2x - 5))

A = (x - 6)(x - 6 - 2x + 5)

A = (x - 6)(-x - 1)

A = -(x - 6)(x + 1)

A = (-x + 6)(x + 1)

A = (6 - x)(x + 1)

✅

B = 9t² - 27t

B = 9t * t - 9t*3

B = 9t(t - 3)

✅

C = -3z + 15

C = 3 * (-z) + 3 * 5

C = 3(5 - z)

✅

* = multiplication

Bonne journée