Question

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

Answer 1

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

Explanation:

`2m^4+6 - am^4-3a`

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

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

`color(white)("XXXX")` `= (2-a)(m^4+3)`