Question

$if space straight A space equals open square brackets table row 1 cell negative 1 end cell row 2 3 end table close square brackets comma space straight B space open square brackets table row 2 cell space 1 end cell row 1 cell space 0 end cell end table close square brackets space comma space verify space that space left parenthesis straight A plus straight B right parenthesis squared space not equal to space straight A squared space plus 2 AB plus straight B squared$

Solution

Here space straight A equals open square brackets table row 1 cell negative 1 end cell row 2 3 end table close square brackets equals open square brackets table row 2 cell space 1 end cell row 1 cell space space 0 end cell end table close square brackets therefore space straight A plus straight B equals space open square brackets table row cell 1 plus 2 end cell cell negative 1 plus 1 end cell row cell 2 plus 1 end cell cell 3 plus 0 end cell end table close square brackets equals open square brackets table row 3 cell space 0 end cell row 3 cell space 3 end cell end table close square brackets space left parenthesis straight A plus straight B right parenthesis squared space space equals space open square brackets table row 3 cell space 0 end cell row 3 cell space 3 end cell end table close square brackets space open square brackets table row 3 cell space 0 end cell row 3 cell space 3 end cell end table close square brackets equals open square brackets table row cell 9 plus 0 end cell cell space 0 plus 0 end cell row cell 9 plus 9 end cell cell space 0 plus 9 end cell end table close square brackets equals open square brackets table row 9 cell space 0 end cell row 18 cell space 9 end cell end table close square brackets space... left parenthesis 1 right parenthesis left parenthesis straight A right parenthesis squared space space space space equals space open square brackets table row 1 cell space minus 1 end cell row 2 cell space 3 end cell end table close square brackets space open square brackets table row 1 cell space minus 1 end cell row 2 cell space space space space 3 end cell end table close square brackets space space space equals open square brackets table row cell 1 minus 2 end cell cell space minus 1 minus 3 end cell row cell 2 plus 6 end cell cell space minus 2 plus 9 end cell end table close square brackets space space space equals open square brackets table row cell negative 1 end cell cell space minus 4 end cell row 8 cell space space space space 7 end cell end table close square brackets 2 AB equals 2 open square brackets table row 2 cell space space minus 1 end cell row 2 cell space 3 end cell end table close square brackets space open square brackets table row 2 cell space 1 end cell row 1 cell space space 0 end cell end table close square brackets equals 2 open square brackets table row cell 4 minus 1 end cell cell space space 2 plus 0 end cell row cell 4 plus 3 end cell cell space space 2 plus 0 end cell end table close square brackets equals 2 open square brackets table row 3 cell space space 2 end cell row cell 7 space end cell 2 end table close square brackets equals open square brackets table row 6 cell space 4 end cell row 14 cell space 4 end cell end table close square brackets space straight B squared equals open square brackets table row 2 cell space 1 end cell row 1 cell space 0 end cell end table close square brackets space open square brackets table row 2 cell space 1 end cell row 1 cell space space 0 end cell end table close square brackets equals open square brackets table row cell 4 plus 1 end cell cell space space 2 plus 0 end cell row cell 2 plus 0 end cell cell space 1 plus 0 end cell end table close square brackets equals open square brackets table row cell 5 space end cell 2 row 2 cell space 1 end cell end table close square brackets space straight A squared plus 2 AB plus straight B squared equals open square brackets table row cell negative 1 end cell cell space minus 4 end cell row 8 7 end table close square brackets plus open square brackets table row 6 cell space 4 end cell row 14 cell space space 4 end cell end table close square brackets plus open square brackets table row 5 cell space 2 end cell row 2 cell space 1 end cell end table close square brackets space space space space space space space space space space space space space space space space space space space space space space space space space equals open square brackets table row cell negative 1 plus 6 plus 5 end cell cell negative 4 plus 4 plus 2 end cell row cell 8 plus 14 plus 2 end cell cell 7 plus 4 plus 2 end cell end table close square brackets equals open square brackets table row 10 cell space 2 end cell row 24 12 end table close square brackets space space space... left parenthesis 2 right parenthesis From space left parenthesis 1 right parenthesis and space left parenthesis 2 right parenthesis comma left parenthesis straight A plus straight B right parenthesis not equal to space straight A squared space plus 2 AB plus straight B squared

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