Answer:
[tex](9x^3+5y^5)(9x^3-5y^5)[/tex]
Step-by-step explanation:
[tex]81x^6-25y^{10}[/tex]
[tex]81=9^2[/tex]
[tex]x^6=x^{3 \cdot 2}=(x^3)^2[/tex]
[tex]\implies 81x^6=(9x^3)^2[/tex]
[tex]25=5^2[/tex]
[tex]y^{10}=y^{5 \cdot 2}=(y^5)^2[/tex]
[tex]\implies 25y^{10}=(5y^5)^2[/tex]
Therefore,
[tex]81x^6-25y^{10}=(9x^3)^2 -(5y^5)^2[/tex]
Apply difference of two squares formula [tex]x^2-y^2=(x+y)(x-y)[/tex]:
[tex]\implies (9x^3)^2 -(5y^5)^2=(9x^3+5y^5)(9x^3-5y^5)[/tex]
