Question

Factor the expression. ( q2 − r2s) ( q4 + q2r2s + r4s2)

Answer 1

(5q2 − r2s)(25q^4+5q^2r^2s+1r^4s^2)

Answer 2

Answer:

$(q^2-r^2s)(q^4+q^2r^2s+r^4s^2)=q^6-r^6s^3$

Step-by-step explanation:

Given : Expression $(q^2-r^2s)(q^4+q^2r^2s+r^4s^2)$

To find : Factor the expression?

Solution :

The given expression $(q^2-r^2s)(q^4+q^2r^2s+r^4s^2)$ is the factored form of $q^6-r^6s^3$  

Now, We solve to get the form

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

Taking RHS and compare with the given expression        

$(q^2-r^2s)(q^4+q^2r^2s+r^4s^2)$    

Where, $a=q^2,b=r^2s$

$=(q^2)^3-(r^2s)^3$

$=q^6-r^6s^3$

Therefore, $(q^2-r^2s)(q^4+q^2r^2s+r^4s^2)=q^6-r^6s^3$