Step-by-step explanation:
Given expression:
- [tex]36a^4 b^{10} - 81a^{16} b^{20}[/tex]
a)
GCF of the terms is:
Factoring:
- [tex]36a^4 b^{10} - 81a^{16} b^{20}=9a^4b^{10}(4 - 9a^{12}b^{10})[/tex]
b)
Difference of squares:
- [tex]36a^4 b^{10} - 81a^{16} b^{20}=(6a^2b^5)^2-(9a^8b^{10})^2=[/tex]
- [tex](6a^2b^5+9a^8b^{10})(6a^2b^5-9a^8b^{10})[/tex]
If you combine both of the methods you will end up with the answer given on the bottom of the question:
- [tex]9a^4b^{10}(4 - 9a^{12}b^{10})=9a^4b^{10}(2 + 3a^6b^5)(2-3a^6b^5)[/tex]
- [tex](6a^2b^5+9a^8b^{10})(6a^2b^5-9a^8b^{10})=9a^4b^{10}(2 + 3a^6b^5)(2-3a^6b^5)[/tex]
