Subject

    গাণিতিক যুক্তি

    Topic

    উৎপাদক

    2b²c² + 2c²a² + 2a²b² - a⁴ - b⁴ - c⁴ এর একটি উৎপাদক-

    ক)
    (- a - b + c)
    খ)
    (a - b - c)
    গ)
    (b - c - a)
    ঘ)
    (a + b - c)

    Explanation

    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)

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