Question

Please help me with this! I got one answer, although I am not sure if it is correct. i think it wants 2 answers

Answer 1

Explanation:

Given expression:

• 
  `36a^4 b^(10) - 81a^(16) b^(20)`

a)

GCF of the terms is:

• 
  `9a^4b^(10)`

Factoring:

• 
  `36a^4 b^(10) - 81a^(16) b^(20)=9a^4b^(10)(4 - 9a^(12)b^(10))`

b)

Difference of squares:

• 
  `36a^4 b^(10) - 81a^(16) b^(20)=(6a^2b^5)^2-(9a^8b^(10))^2=`
• 
  `(6a^2b^5+9a^8b^(10))(6a^2b^5-9a^8b^(10))`

If you combine both of the methods you will end up with the answer given on the bottom of the question:

• 
  `9a^4b^(10)(4 - 9a^(12)b^(10))=9a^4b^(10)(2 + 3a^6b^5)(2-3a^6b^5)`
• 
  `(6a^2b^5+9a^8b^(10))(6a^2b^5-9a^8b^(10))=9a^4b^(10)(2 + 3a^6b^5)(2-3a^6b^5)`