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By using properties of determinants. Sho...

By using properties of determinants. Show that:
(i) `|[a-b-c,2a,2a],[2b,b-c-a,2b],[2c,2c,c-a-b]|=(a+b+c)^3`
(ii) `|[x+y+2z, x, y],[ z, y+z+2x, y],[ z, x, z+x+2y]|=2(x+y+z)^3`

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To solve the given determinants using properties of determinants, we will proceed step by step for both parts of the question. ### Part (i) We need to show that: \[ \left| \begin{array}{ccc} a - b - c & 2a & 2a \\ 2b & b - c - a & 2b \\ ...
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