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Hello, I have been trying to solve the top line equation to get the result (the bottom line). I am searching for a clue (the steps) on how to obtain those four brackets as a result.
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factoring the expression within the radical just involves the difference of squares ...
$4d^2R^2 - (d^2-r^2+R^2)$
$(2dR)^2 - (d^2-r^2+R^2)^2$
$[2dR -(d^2-r^2+R^2)] \cdot [2dR + (d^2-r^2+R^2)]$
$[-(d^2-2dR+R^2) + r^2] \cdot [(d^2+2dR+R^2) - r^2]$
$[r^2-(d-R)^2] \cdot [(d+R)^2 - r^2]$
$[(r-d+R)(r+d-R)] \cdot [(d+R-r)(d+R+r)]$
multiply the two middle factors by (-1) ...
$(-d+r+R)(-d-r+R)(-d+r-R)(d+r+R)$