Question

Aratati ca propria aceasta este adevarata oricare ar fii x:
(2x-5)²+(2x-5)(2x+5)+(2x+5)²-37=12(x-1)(x+1)

Dau coroana

Answer 1

(2x-5)²+(2x-5)(2x+5)+(2x+5)²-37 =
= ( (2x-5)+(2x+5) )² - (2x-5)(2x+5) - 37 =
= (4x)² - (2x-5)(2x+5) - 37 =
= (4x)² - ( (2x)² -5²) - 37 =
= (4x)² - (2x)² + 25 - 37 =
= (4x-2x)(4x+2x) - 12 =
= (2x)(6x) - 12 =
= 12x² - 12 =
= 12(x²-1) =
= 12(x-1)(x+1)