Answer:
[tex](5x^2-2)(25x^4+10x^2+4)[/tex]
Step-by-step explanation:
Given expression,
[tex]125x^6-8[/tex]
[tex]=(5)^3 (x^2)^3 -2^3[/tex] [tex]\because (ab)^m=a^mb^m\text{ and }a^{mn}=(a^m)^n[/tex]
[tex]=(5x^2)^3+(-2)^3[/tex]
By using a³ + b³ = (a-b) (a² -ab + b² )
[tex]=(5x^2+(-2)) ((5x^2)^2 - (5x^2\times -2) + (-2)^2)[/tex]
[tex]=(5x^2-2)(25x^4+10x^2+4)[/tex]
Which is the required factor form,
Third option is correct.
