SOLUTION: hi. i need some help in performing this indicated operation and simplifying it: 27a^k - 9a^k+2 + 15a^k+4/3a^k thanks!

Algebra ->  Equations -> SOLUTION: hi. i need some help in performing this indicated operation and simplifying it: 27a^k - 9a^k+2 + 15a^k+4/3a^k thanks!      Log On


   

Question 190299: hi.
i need some help in performing this indicated operation and simplifying it:
27a^k - 9a^k+2 + 15a^k+4/3a^k
thanks!
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Is the expression %2827a%5Ek+-+9a%5E%28k%2B2%29+%2B+15a%5E%28k%2B4%29%29%2F%283a%5Ek%29???


%2827a%5Ek+-+9a%5E%28k%2B2%29+%2B+15a%5E%28k%2B4%29%29%2F%283a%5Ek%29 Start with the given expression


%2827a%5Ek+-+9a%5Ek%2Aa%5E2+%2B+15a%5Ek%2Aa%5E4%29%2F%283a%5Ek%29 Factor a%5E%28k%2B2%29 into a%5Ek%2Aa%5E2. Factor a%5E%28k%2B4%29 into a%5Ek%2Aa%5E4


Note: use the identity x%5E%28y%2Bz%29=x%5Ey%2Ax%5Ez


%283a%5Ek%2A%289+-+3a%5E2+%2B+5a%5E4%29%29%2F%283a%5Ek%29 Factor out the GCF 3a%5Ek from the numerator


%28highlight%283a%5Ek%29%289+-+3a%5E2+%2B+5a%5E4%29%29%2F%28highlight%283a%5Ek%29%29 Highlight the common terms.


%28cross%283a%5Ek%29%289+-+3a%5E2+%2B+5a%5E4%29%29%2F%28cross%283a%5Ek%29%29 Cancel out the common terms.


9+-+3a%5E2+%2B+5a%5E4 Simplify


5a%5E4-3a%5E2%2B9 Rearrange the terms.


So %2827a%5Ek+-+9a%5E%28k%2B2%29+%2B+15a%5E%28k%2B4%29%29%2F%283a%5Ek%29=5a%5E4-3a%5E2%2B9 where a%3C%3E0