Difficulty:40%
Factorize a⁴+b⁴+c⁴-2a²b²-2b²c²-2c²a²
MQ18---Factorization
2012-02-18 5:14 am
回答 (2)
2012-02-18 5:42 am
✔ 最佳答案
a⁴ + b⁴ + c⁴ - 2a²b² - 2b²c² - 2a²c²= a⁴ + b⁴ + c⁴ - 2a²b² - 2b²c² + 2a²c² - 4a²c²
= (a⁴ - 2a²b² + b⁴) + 2a²c² - 2b²c² + c⁴- 4a²c²
= (a² - b²)² + 2c²(a² - b²) + c⁴- 4a²c²
= (a² - b² + c²)² - (2ac)²
= (a² - b² + c² + 2ac) (a² - b² + c² - 2ac)
= ( (a + c)² - b² ) ( (a - c)² - b² )
= (a + b + c)(a - b + c) (a + b - c)(a - b - c)
2012-02-18 5:27 am
(a - b - c) (a + b - c) (a - b + c) (a + b + c)
收錄日期: 2021-04-13 18:32:38
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