Answer:
[tex](p-6q)(p^2+6pq+36pq^2)[/tex]
Step-by-step explanation:
[tex]p^3-216q^3[/tex]
Rewrite [tex]p^3-216q^3[/tex] as [tex]p^3-(6q)^3[/tex]:
[tex]p^3-216q^3[/tex]
Rewrite 216 as [tex]6^3[/tex]
[tex]=p^3-6^3q^3[/tex]
Apply exponent rule: [tex]a^mb^m=(ab)^m[/tex]
[tex]6^3q^3=(6q)^3[/tex]
[tex]=p^3-(6q)^3[/tex]
[tex]=p^3-(6q)^3[/tex]
Apply difference of cubes formula: [tex]x^3-y^3=(x-y)(x^2+xy+y^2)[/tex]
[tex]p^3-(6q)^3=(p-6q)(p^2+6pq+6^2q^2)[/tex]
[tex]=(p-6q)(p^2+6pq+6^2q^2)[/tex]
Refine.
[tex]=(p-6q)(p^2+6pq+36q^2)[/tex]
