5.108
1)
(а² + в²) = (а²)³ + 3*(а²)²*в² + 3*а²*(в²)² + (в²)³ = а⁶ + 3а⁴в² + 3а²в⁴ + в⁶,
2)
(х² - у²) = (х²)³ - 3*(х²)²*у² + 3*х²*(у²)² + (у²)³ = х⁶ - 3х⁴у² + 3х²у⁴ + у⁶,
3)
(2m² - 3n²)³ = (2m²)³ - 3*(2m²)²*3n² + 3*2m²*(3n²)² + (3n²)³ =
= 8m⁶ - 36m⁴n² + 54m²n⁴ + 27n⁶,
4)
(2a³ - 3b²)³ = (2a³)³ - 3*(2a³)²*3b² + 3*2a³*(3b²)² + (3b²)³ =
= a⁹ - 36a⁶b² + 54a³3b⁴ + 27b⁶,
5)
(4m³ + 5n²)³ = (4m³)³ + 3*(4m³)²*5n² + 3*4m³*(5n²)² + (5n²)³ =
= 64m⁹ + 240m⁶n² + 300m³n⁴ + 125n⁶,
6)
(10p⁴ - 6q²) = (10p⁴)³ - 3*(10p⁴)²*6q² + 3*10p⁴*(6q²)² + (6q²)³ =
= 1000p¹² - 1800p⁸q² + 1080p⁴*q⁴ + 216q⁶,
7)
(7u³ - 9v⁴)³ = (7u³)³ - 3*(7u³)²*9v⁴ + 3*7u³*(9v⁴)² + (9v⁴)³ =
= 343u⁹ - 1323u⁶v⁴ + 1701u³9v⁸ + 729v¹²,
8)
(10x³ + 3y²)³ = (10х³)³ + 3*(10х³)²*3у² + 3*10х³*(3у²)² + (3у²)³ =
= 1000х⁹ + 900х⁶у² + 270х³у⁴ + 27у⁶,
5.109
а³ + 3ав(а + в) + в³ = (а + в)³,
а³ + 3а²в + 3ав² + в³ = (а + в)³,
(а + в)³ = (а + в)³,
а³ - 3ав(а - в) - в³ = (а - в)³,
а³ - 3а²в + 3ав² - в³ = (а - в)³,
(а - в)³ = (а - в)³
Copyright © 2024 SCHOLAR.TIPS - All rights reserved.
Answers & Comments
5.108
1)
(а² + в²) = (а²)³ + 3*(а²)²*в² + 3*а²*(в²)² + (в²)³ = а⁶ + 3а⁴в² + 3а²в⁴ + в⁶,
2)
(х² - у²) = (х²)³ - 3*(х²)²*у² + 3*х²*(у²)² + (у²)³ = х⁶ - 3х⁴у² + 3х²у⁴ + у⁶,
3)
(2m² - 3n²)³ = (2m²)³ - 3*(2m²)²*3n² + 3*2m²*(3n²)² + (3n²)³ =
= 8m⁶ - 36m⁴n² + 54m²n⁴ + 27n⁶,
4)
(2a³ - 3b²)³ = (2a³)³ - 3*(2a³)²*3b² + 3*2a³*(3b²)² + (3b²)³ =
= a⁹ - 36a⁶b² + 54a³3b⁴ + 27b⁶,
5)
(4m³ + 5n²)³ = (4m³)³ + 3*(4m³)²*5n² + 3*4m³*(5n²)² + (5n²)³ =
= 64m⁹ + 240m⁶n² + 300m³n⁴ + 125n⁶,
6)
(10p⁴ - 6q²) = (10p⁴)³ - 3*(10p⁴)²*6q² + 3*10p⁴*(6q²)² + (6q²)³ =
= 1000p¹² - 1800p⁸q² + 1080p⁴*q⁴ + 216q⁶,
7)
(7u³ - 9v⁴)³ = (7u³)³ - 3*(7u³)²*9v⁴ + 3*7u³*(9v⁴)² + (9v⁴)³ =
= 343u⁹ - 1323u⁶v⁴ + 1701u³9v⁸ + 729v¹²,
8)
(10x³ + 3y²)³ = (10х³)³ + 3*(10х³)²*3у² + 3*10х³*(3у²)² + (3у²)³ =
= 1000х⁹ + 900х⁶у² + 270х³у⁴ + 27у⁶,
5.109
1)
а³ + 3ав(а + в) + в³ = (а + в)³,
а³ + 3а²в + 3ав² + в³ = (а + в)³,
(а + в)³ = (а + в)³,
2)
а³ - 3ав(а - в) - в³ = (а - в)³,
а³ - 3а²в + 3ав² - в³ = (а - в)³,
(а - в)³ = (а - в)³