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![Prove that |[a - b - c, 2a, 2a],[2b, b - c - a, 2b],[2c, 2c, c - a - b]| = (a + b +c)^3](http://i.ytimg.com/vi/F6Kll3fQIB0/mqdefault.jpg "Prove that |[a - b - c, 2a, 2a],[2b, b - c - a, 2b],[2c, 2c, c - a - b]| = (a + b +c)^3")
![Show without expanding : |[(a - 1)^2, a^2 + 1, a],[(b - 1)^2, b^2 + 1, b],[(c - 1)^2, c^2, c]| = 0](http://i.ytimg.com/vi/F2NjzxVbU60/mqdefault.jpg "Show without expanding : |[(a - 1)^2, a^2 + 1, a],[(b - 1)^2, b^2 + 1, b],[(c - 1)^2, c^2, c]| = 0")
![One root of the equation | x + a, b, c],[b, x + c, a],[c, a, x + b]| = 0 is](http://i.ytimg.com/vi/jsu2fJ_645g/mqdefault.jpg "One root of the equation | x + a, b, c],[b, x + c, a],[c, a, x + b]| = 0 is")
![Show without expanding at any stage that |[1, bc, a(b + c)],[1, ca, b(c + a)],[1, ab, c(a + b)]| = 0](http://i.ytimg.com/vi/xvhKpsuwUoA/mqdefault.jpg "Show without expanding at any stage that |[1, bc, a(b + c)],[1, ca, b(c + a)],[1, ab, c(a + b)]| = 0")