How do you factor $25 g^{3} v^{3} + 15 g^{2} e^{3} v^{3} + 5 g b d + 3 e^{3} b d$ $25 g^3 v^3 + 15 g^2 e^3 v^3 + 5 g b d + 3 e^3 b d$ ?

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How do you factor $25 g^{3} v^{3} + 15 g^{2} e^{3} v^{3} + 5 g b d + 3 e^{3} b d$ $25 g^3 v^3 + 15 g^2 e^3 v^3 + 5 g b d + 3 e^3 b d$ ?

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Answer 1 · 2016-06-22T12:59:26

$25 g^{3} v^{3} + 15 g^{2} e^{3} v^{3} + 5 g b d + 3 e^{3} b d = (5 g^{2} v^{3} + b d) (5 g + 3 e^{3})$ $25g^3v^3+15g^2e^3v^3+5gbd+3e^3bd=color(blue)((5g^2v^3+bd)(5g+3e^3))$

Explanation:

Note 1:
$XXX$ $color(white)("XXX")$ The first two terms have a common factor of
$XXXXXX 5 g^{2} v^{3}$ $color(white)("XXXXXX")5g^2v^3$
$XXX 25 g^{3} v^{3} + 15 g^{2} e^{3} v^{3} = (5 g^{2} v^{3}) (5 g + 3 e^{3})$ $color(white)("XXX")25g^3v^3+15g^2e^3v^3=(color(red)(5g^2v^3))(5g+3e^3)$

Note 2:
$XXX$ $color(white)("XXX")$ The last two terms have a common factor of
$XXXXXX b d$ $color(white)("XXXXXX")bd$
$XXX 5 g b d + 3 e^{3} b d = (b d) (5 g + 3 e^{3})$ $color(white)("XXX")5gbd+3e^3bd=(color(green)(bd))(5g+3e^3)$

Therefore:
$XXX 25 g^{3} v^{3} + 15 g^{2} e^{3} v^{3} + 5 g b d + 3 e^{3} b d$ $color(white)("XXX")25g^3v^3+15g^2e^3v^3+5gbd+3e^3bd$
$XXXXXX = (5 g^{2} v^{3}) (5 g + 3 e^{3}) + (b d) (5 g + 3 e^{3})$ $color(white)("XXXXXX")=(color(red)(5g^2v^3))(5g+3e^3)+(color(green)(bd))(5g+3e^3)$

Note 3:
$XXX$ $color(white)("XXX")$ The second factor for each term is identical

$XXX 25 g^{3} v^{3} + 15 g^{2} e^{3} v^{3} + 5 g b d + 3 e^{3} b d$ $color(white)("XXX")25g^3v^3+15g^2e^3v^3+5gbd+3e^3bd$
$XXXXXX = (5 g^{2} v^{3} + b d) (5 g + 3 e^{3})$ $color(white)("XXXXXX")=(color(red)(5g^2v^3)+color(green)(bd))(5g+3e^3)$

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How do you factor $25 g^{3} v^{3} + 15 g^{2} e^{3} v^{3} + 5 g b d + 3 e^{3} b d$ $25 g^3 v^3 + 15 g^2 e^3 v^3 + 5 g b d + 3 e^3 b d$ ?

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How do you factor 25 g^3 v^3 + 15 g^2 e^3 v^3 + 5 g b d + 3 e^3 b d25g3v3+15g2e3v3+5gbd+3e3bd25 g^3 v^3 + 15 g^2 e^3 v^3 + 5 g b d + 3 e^3 b d?

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How do you factor $25 g^{3} v^{3} + 15 g^{2} e^{3} v^{3} + 5 g b d + 3 e^{3} b d$ $25 g^3 v^3 + 15 g^2 e^3 v^3 + 5 g b d + 3 e^3 b d$ ?