Question

What is the factored form of r27-s30?

Answer 1

This is what I get   First is to get them to perfect squares .  R27 = r9^3 S30= s10^3 =(a-b)(a^2+ab+b^2) Where a=r9 and b=s10  (R9-s10)((r9)^2+r9+s10+(s10)^2)  Now simplify To get   (R9-s10)(r18-r9+s10+s20)

Answer 2

Answer:

Factored Form:

$\Rightarrow (r^9-s^{10})(r^{18}+r^9s^{10}+s^{20})$

Step-by-step explanation:

Given: $r^{27}-s^{30}$

We need to factor the expression

$\Rightarrow (r^{9})^3-(s^{10})^3$

$a^3-b^3=(a-b)(a^2+ab+b^2)$

$a\rightarrow r^9$

$b\rightarrow s^{10}$

$(r^{9})^3-(s^{10})^3=(r^9-s^{10})((r^9)^2+r^9\cdot s^{10}+(s^{10})^2)$

$\Rightarrow (r^9-s^{10})(r^{18}+r^9s^{10}+s^{20})$

Hence, In factored form $\Rightarrow (r^9-s^{10})(r^{18}+r^9s^{10}+s^{20})$