Prove that `| ((b+c)^2, a^2,a^2),(b^2,(c+a)^2,b^2),(c^2,c^2,(a+b)^2)|=2abc(a+b+c)^3`

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det [[a - b - c, 2a, 2a], [2b, b - c - a, 2b], [2c, 2c, c - a - b]] = (a + b + c) ^ 3 det [[a - b - c, 2a, 2a], [2b, b - c - a, 2b], [2c, 2c, c - a - b]] = (a + b + c) ^ 3
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Prove: |(a^2,b c, a c+c^2),(a^2+a b,b^2,a c ),(a b,b^2+b c,c^2)|=4a^2b^2c^2 | 12 | DETERMINANTS ... Prove: |(a^2,b c, a c+c^2),(a^2+a b,b^2,a c ),(a b,b^2+b c,c^2)|=4a^2b^2c^2 | 12 | DETERMINANTS ...
L-31| vector| [ a+b b+c c+a] = 2 [ a b c ] L-31| vector| [ a+b b+c c+a] = 2 [ a b c ]