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How do you factor by grouping $2 m^{4} + 6 - a m^{4} - 3 a$ $2m^4 + 6 - am^4 - 3a$ ?

1 Answer

Jul 23, 2015

Extract factors from $2 m^{4} + 6$ $2m^4+6$ and $- a m^{4} - 3 a$ $-am^4-3a$ leaving a factor common to both; then extract that factor:
$XXXX$ $color(white)("XXXX")$ $2 m^{4} + 6 - a m^{4} - 3 a = (2 - a) (m^{4} + 3)$ $2m^4+6-am^4-3a = (2-a)(m^4+3)$

Explanation:

$2 m^{4} + 6 - a m^{4} - 3 a$ $2m^4+6 - am^4-3a$

$XXXX$ $color(white)("XXXX")$ $= (2 m^{4} + 6) - (a m^{4} + 3 a)$ $= (color(red)(2m^4+6)) - (color(blue)(am^4+3a))$

$XXXX$ $color(white)("XXXX")$ $= 2 (m^{4} + 3) - a (m^{4} + 3)$ $=color(red)(2)(m^4+3) - color(blue)a(m^4+3)$

$XXXX$ $color(white)("XXXX")$ $= (2 - a) (m^{4} + 3)$ $= (2-a)(m^4+3)$

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