Bonjour,

B=(5x-2)²+(5x-2)(3x+7)

 =(5x-2)(3x+7+5x-2)

 =(5x-2)(8x+5)

 =40x²+25x-16x-10

B=40x²+9x-10

bjr

Soit B = (5x – 2)² + (5x – 2)(3x + 7)

1) Développer, réduire et ordonner B.

(5x – 2)² + (5x – 2)(3x + 7)  =

(5x)² - 2*5x*2 + 2² + 5x*3x + 5x*7 - 2*3x - 2x7=

25x² - 20x + 4 + 15x² + 35x - 6x - 14 =

25x² + 15x²- 20x + 35x - 6x  + 4 - 14 =

40x² + 9x² - 10

2) si on demande de factoriser

(5x – 2)² + (5x – 2)(3x + 7)  =

(5x – 2)(5x - 2) + (5x – 2)(3x + 7) =

(5x – 2)(5x - 2) + (5x – 2)(3x + 7) =

(5x – 2)[(5x - 2) + (3x + 7) ] =

(5x - 2)(8x + 5)