192k views
0 votes
Factor 27a^3 b^9+8c^18

User Qfwfq
by
8.3k points

1 Answer

2 votes

For this case we must factor the following expression:


27a ^ 3b ^ 9 + 8c ^ 18

So, we rewrite the terms like:


27a ^ 3b ^ 9 = (3ab ^ 3) ^ 3\\8c ^ {18} = (2c ^ 6) ^ 3

So, we have:


(3ab ^ 3) ^ 3 + (2c^6) ^ 3 =

Being both perfect cube terms, we factorize by applying the cube sum formula:


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

Where:


a = 3ab ^ 3\\b = 2c ^ 6\\(3ab ^ 3 + 2c ^ 6) ((3ab ^ 3) ^ 2- (3ab ^ 3) (2c ^ 6) + (2c ^ 6) ^ 2) =\\(3ab ^ 3 + 2c ^ 6) (9a^2b ^ 6-6ab ^ 3c ^ 6 + 4c ^ {12})

Answer:


(3ab ^ 3 + 2c ^ 6) (9a2b ^ 6-6ab ^ 3c ^ 6 + 4c ^ 12)

User Tatarinho
by
7.6k points

Related questions

asked May 28, 2020 208k views
David Snowsill asked May 28, 2020
by David Snowsill
8.3k points
1 answer
5 votes
208k views
1 answer
8 votes
79.3k views
asked Oct 22, 2024 83.5k views
ElasticThoughts asked Oct 22, 2024
by ElasticThoughts
7.8k points
1 answer
4 votes
83.5k views