Verified answer

a³ + b³ = (a + b)(a² - ab + b²)

(a - b)² = a² - 2ab + b²

(43³ + 32³)/75 - 43*32 = (43 + 32)(43² - 43*32 + 32²)/75 - 43*32 =

75* (43² - 43*32 + 32²)/75 - 43*32 =   43² - 43*32 + 32² - 43*32 =  

43² - 2*43*32 + 32²  = (43 - 32)² = (11)² = 121