Factor completely
[tex]21b^4+5b^2m^2-4m^4[/tex]We need to split the expression into convenient groups
[tex]21b^4+5b^2m^2-4m^4=21b^4+12b^2m^2-4m^4-7b^2m^2[/tex]Factor 3b^2 from the first group and -m^2 from the second group:
[tex]21b^4+5b^2m^2-4m^4=3b^2(7b^2+4m^2)-m^2(4m^2+7b^2)[/tex]Factor out the common term 7b^2+4m^2:
[tex]21b^4+5b^2m^2-4m^4=(3b^2-m^2)(4m^2+7b^2)[/tex]This is the final factorization
