(a ^ 4 * b ^ 54 * b ^ 6 - a ^ 5 * c ^ 6 * d ^ 7) ^ 3 =?
Ответы
Ответ:
-a¹²(ac⁶d⁷ - b⁶⁰)³ или a¹²b¹⁸⁰ - a¹³c¹⁸d²¹
Объяснение:
(a⁴b⁵⁴ × b⁶ - a⁵c⁶d⁷)³ = (a⁴b⁶⁰ - a⁵c⁶d⁷)³ = ((a⁴(b⁶⁰ - ac⁶d⁷))³ = a¹²(b⁶⁰ - ac⁶d⁷)³ = a¹²((b⁶⁰)³ - 3(b⁶⁰)² × ac⁶d⁷ + 3b⁶⁰ × (ac⁶d⁷)² - (ac⁶d⁷)³) = a¹²(b¹⁸⁰ - 3ab¹²⁰c⁶d⁷ + 3a²b⁶⁰c¹²d¹⁴ - a³c¹⁸d²¹) = a¹²(3ab⁶⁰c⁶d⁷(ac⁶d⁷ - b⁶⁰) + (b¹⁸⁰ - a³c¹⁸d²¹)) = a¹²(3ab⁶⁰c⁶d⁷(ac⁶d⁷ - b⁶⁰) + ((b⁶⁰)³ - (ac⁶d⁷)³)) = a¹²(3ab⁶⁰c⁶d⁷(ac⁶d⁷ - b⁶⁰) + (b⁶⁰ - ac⁶d⁷)(b¹²⁰ + ab⁶⁰c⁶d⁷ + a²c¹²d¹⁴)) = a¹²(3ab⁶⁰c⁶d⁷(ac⁶d⁷ - b⁶⁰) - (ac⁶d⁷ - b⁶⁰)(b¹²⁰ + ab⁶⁰c⁶d⁷ + a²c¹²d¹⁴)) = a¹²(ac⁶d⁷ - b⁶⁰)(3ab⁶⁰c⁶d⁷ - b¹²⁰ - ab⁶⁰c⁶d⁷ - a²c¹²d¹⁴) = a¹²(ac⁶d⁷ - b⁶⁰)(-b¹²⁰ + 2ab⁶⁰c⁶d⁷ - a²c¹²d¹⁴) = -a¹²(ac⁶d⁷ - b⁶⁰)(b¹²⁰ - 2ab⁶⁰c⁶d⁷ + a²c¹²d¹⁴) = -a¹²(ac⁶d⁷ - b⁶⁰)(b⁶⁰ - ac⁶d⁷)² = -a¹²(ac⁶d⁷ - b⁶⁰)(ac⁶d⁷ - b⁶⁰)² = -a¹²(ac⁶d⁷ - b⁶⁰)³ = a¹²b¹⁸⁰ - a¹³c¹⁸d²¹