bonjour
on cherche un facteur commun
(5x + 2)² + (x + 7)(5x + 2) - 25x² + 4 =
(5x + 2)² + (x + 7)(5x + 2) - (25x² - 4) =
(5x + 2)² + (x + 7)(5x + 2) - [ (5x)² - 2²] =
(5x + 2)² + (x + 7)(5x + 2) - [ (5x + 2)(5x - 2)] =
(5x + 2)(5x + 2) + (x + 7)(5x + 2) - (5x + 2)(5x - 2) =
la facteur commun est (5x + 2)
(5x + 2)(5x + 2) + (x + 7)(5x + 2) - (5x + 2)(5x - 2) =
(5x + 2) [(5x + 2) + (x + 7)) - (5x - 2) ] =
(5x + 2)(5x + 2 + x + 7 - 5x + 2) =
(5x + 2)(x + 11)
