Answer:
Factored Form:
[tex] \Rightarrow (r^9-s^{10})(r^{18}+r^9s^{10}+s^{20})[/tex]
Step-by-step explanation:
Given: [tex]r^{27}-s^{30}[/tex]
We need to factor the expression
[tex]\Rightarrow (r^{9})^3-(s^{10})^3[/tex]
[tex]a^3-b^3=(a-b)(a^2+ab+b^2)[/tex]
[tex]a\rightarrow r^9[/tex]
[tex]b\rightarrow s^{10}[/tex]
[tex] (r^{9})^3-(s^{10})^3=(r^9-s^{10})((r^9)^2+r^9\cdot s^{10}+(s^{10})^2)[/tex]
[tex] \Rightarrow (r^9-s^{10})(r^{18}+r^9s^{10}+s^{20})[/tex]
Hence, In factored form [tex] \Rightarrow (r^9-s^{10})(r^{18}+r^9s^{10}+s^{20})[/tex]
