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

Please help me with this! I got one answer, although I am not sure if it is correct-example-1
User Pawan Maheshwari
by
2.8k points

1 Answer

19 votes
19 votes

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)
User DurkoMatko
by
3.1k points