Réponses

2013-12-01T18:46:42+01:00
1. (7-x)²-4
= ((7-x)-2)((7-x)+2)
= (5-x)(9-x)

2. (3x-5)²-(x+4)²
= ((3x-5)-(x+4))((3x-5)+(x+4))
= (2x-9)(4x-1)

3. 4(x-5)²-9(x-3)²
= 4(x²-10x+25)-9(x²-6x+9)
= (4x²-40x+100)-(9x²-54x+81)
= (2x-10)²-(3x-9)²
= ((2x-10)-(3x-9))((2x-10)+(3x-9))
= (-x-1)(5x-19)

4. 4x²-8
= 2(2x²-4)

5. 9x²-24x+16
= (3x-4)²

6. (3x-6)(x+5)-(x-2)(x-5)
= (x-5)[(3x-6)-(x-2)]
= (x-5)(2x-4)

7. 4x²-81+(4x-18)(x-5)
= (2x-9)(2x+9)+
(4x-18)(x-5)
= (2x-9)(2x+9)+2(2x-9)(x-5)
= (2x-9)[(2x+9)+2(x-5)]
= (2x-9)(4x-1)