2b²c² + 2c²a² + 2a²b² - a⁴ - b⁴ - c⁴ এর একটি উৎপাদক-
A (- a - b + c)
B (a - b - c)
C (b - c - a)
D (a + b - c)
Solution
Correct Answer: Option D
2b²c² + 2c²a² + 2a²b² - a⁴ - b⁴ - c⁴
= 4b²c² - (a⁴ + b⁴ + c⁴ + 2b²c² - 2c²a² - 2a²b²)
= (2bc)² - (a² - b² - c²)²
= (2bc + a² - b² - c²) (2bc - a² + b² + c²)
= (a² - b² - c² + 2bc) (- a² + b² + c² + 2bc)
= [a² - (b - c)²] [(b + c)² - a²]
= (a + b - c) (a - b + c) (b + c + a) (b + c - a)
= (a + b - c) (a - b + c) (a + b + c) (- a + b + c)