Question

$By space using space properties space of space determinants comma space show space that open vertical bar table row cell straight x plus 4 end cell cell 2 space straight x end cell cell 2 space straight x end cell row cell 2 space straight x end cell cell space space straight x plus 4 end cell cell 2 space straight x end cell row cell 2 space straight x end cell cell 2 space straight x end cell cell space space straight x plus 4 end cell end table close vertical bar space equals space left parenthesis 5 space straight x plus 4 right parenthesis space left parenthesis 4 minus straight x right parenthesis squared$

Solution

straight L. straight H. straight S space equals open vertical bar table row cell straight x plus 4 end cell cell 2 space straight x end cell cell 2 space straight x end cell row cell 2 space straight x end cell cell space space straight x plus 4 end cell cell 2 space straight x end cell row cell 2 space straight x end cell cell 2 space straight x end cell cell space space straight x plus 4 end cell end table close vertical bar space space space space space space space space space space space space equals space space open vertical bar table row cell 5 straight x plus 4 end cell cell space space 2 space straight x end cell cell 2 space straight x end cell row cell 5 straight x plus 4 end cell cell space space space straight x plus 4 end cell cell 2 space straight x end cell row cell 5 straight x plus 4 end cell cell 2 space straight x end cell cell space space straight x plus 4 end cell end table close vertical bar space comma space by space straight C subscript 1 plus straight C subscript 2 plus straight C subscript 3 space space space space space space space space space space space equals space space space left parenthesis 5 straight x plus 4 right parenthesis space space open vertical bar table row 1 cell 2 space straight x end cell cell 2 space straight x end cell row 1 cell space space space straight x plus 4 end cell cell 2 space straight x end cell row 1 cell 2 space straight x end cell cell space space straight x plus 4 end cell end table close vertical bar space space space space space space space space space space space space equals space space space left parenthesis 5 straight x plus 4 right parenthesis space space open vertical bar table row 1 cell 2 space straight x end cell cell 2 space straight x end cell row 1 cell space space space straight x plus 4 end cell cell 2 space straight x end cell row 1 cell 2 space straight x end cell cell space space straight x plus 4 end cell end table close vertical bar space by space straight R subscript 2 minus straight R subscript 1 space comma space straight R subscript 3 minus straight R subscript 1 space space space space space space space space space space space equals space space space left parenthesis 5 straight x plus 4 right parenthesis space space open curly brackets left parenthesis 1 right parenthesis left parenthesis 4 minus straight x right parenthesis left parenthesis 4 minus straight x right parenthesis close curly brackets space space space space space space space space space space space equals space space space left parenthesis 5 straight x plus 4 right parenthesis space space left parenthesis 4 minus straight x right parenthesis squared

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