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By using properties of determinants. Sho...

By using properties of determinants. Show that:
(i) `|(x+4,2x,2x),(2x,x+4,2x),(2x,2x,x+4)|=(5x-4)(4-x)^2`
(ii) `|(y+k,y,y),(y,y+k,y),(y,y,y+k)|=k^2(3y+k)`

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To solve the given determinants using properties of determinants, we will follow a step-by-step approach. ### Part (i) We need to show that: \[ \left| \begin{array}{ccc} x+4 & 2x & 2x \\ 2x & x+4 & 2x \\ ...
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