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Prove that : |{:((y+z)^(2),x^(2),x^(2)),...

Prove that : `|{:((y+z)^(2),x^(2),x^(2)),(y^(2),(x+z)^(2),y^(2)),(z^(2),z^(2),(x+y)^(2)):}|=2xyz (x+y+z)^(3)`

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AI Generated Solution

To prove the determinant identity given in the question, we will follow a systematic approach. **Given:** We need to prove that: \[ | \begin{vmatrix} (y+z)^2 & x^2 & x^2 \\ y^2 & (x+z)^2 & y^2 \\ ...
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