Note 1:
color(white)("XXX")The first two terms have a common factor of
color(white)("XXXXXX")5g^2v^3
color(white)("XXX")25g^3v^3+15g^2e^3v^3=(color(red)(5g^2v^3))(5g+3e^3)
Note 2:
color(white)("XXX")The last two terms have a common factor of
color(white)("XXXXXX")bd
color(white)("XXX")5gbd+3e^3bd=(color(green)(bd))(5g+3e^3)
Therefore:
color(white)("XXX")25g^3v^3+15g^2e^3v^3+5gbd+3e^3bd
color(white)("XXXXXX")=(color(red)(5g^2v^3))(5g+3e^3)+(color(green)(bd))(5g+3e^3)
Note 3:
color(white)("XXX")The second factor for each term is identical
color(white)("XXX")25g^3v^3+15g^2e^3v^3+5gbd+3e^3bd
color(white)("XXXXXX")=(color(red)(5g^2v^3)+color(green)(bd))(5g+3e^3)