Question:উৎপাদকে বিশ্লেষণ কর: `2b^2c^2 + 2c^2a^2 + 2a^2b^2 - a^4 - b^4 - c^4`
Answer `2b^2c^2 + 2c^2a^2 + 2a^2b^2 - a^4 - b^4 - c^4` `= 4a^2b^2 - a^4 - b^4 - c^4 - 2a^2b^2 + 2b^2c^2 + 2c^2a^2` `= 4a^2b^2 - (a^4 + b^4 + c^4 + 2a^2b^2 - 2b^2c^2 - 2c^2a^2)` `= 4a^2b^2 - {(a^2)^2 + (b^2)^2 + (-c^2)^2 + 2a^2b^2 + 2b^2` `(-c^2) + (-c^2)a^2}` `= (2ab)^2 - (a^2 + b^2 - c^2)^2` `= (2ab + a^2 + b^2 - c^2) (2ab - a^2 - b^2 + c^2)` `= {(a^2 + 2ab + b^2) - c^2} {c^2 - (a^2 - 2ab + b^2)}` `= {(a + b)^2 - c^2} {c^2 - (a - b)^2}` `= (a + b + c) (a + b - c) (c + a - b) (c - a + b)` `= (a + b + c) (a + b - c) (b + c - a) (c + a - b)` `= (a + b + c) (b + c - a) (c + a - b) (a + b - c)` (Ans)
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utpadoke bisholeshn karo: `2b^2c^2 + 2c^2a^2 + 2a^2b^2 - a^4 - b^4 - c^4`