SOLUTION: Simplify. 7x√ [ (x + y)3] – 5x2√(x + y) The last question of the day, my day anyway!! I come up with 2 different answers and they both seem too long. Can you he

Algebra ->  Square-cubic-other-roots -> SOLUTION: Simplify. 7x√ [ (x + y)3] – 5x2√(x + y) The last question of the day, my day anyway!! I come up with 2 different answers and they both seem too long. Can you he      Log On


   

Question 288200: Simplify. 7x√ [ (x + y)3] – 5x2√(x + y)
The last question of the day, my day anyway!! I come up with 2 different answers and they both seem too long. Can you help?
Cynthia
Found 2 solutions by richwmiller, jim_thompson5910:
Answer by richwmiller(17219) About Me  (Show Source):
You can put this solution on YOUR website!
Is this the problem?
+7x%2Asqrt%28+%28x+%2B+y%29%5E3%29 – 5x%5E2sqrt%28x+%2B+y%29
It is very involved. Double check everything.

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Let's assume that every variable is positive.


7x%2Asqrt%28%28x%2By%29%5E3%29-5x%5E2%2Asqrt%28x%2By%29 Start with the given expression.


7x%2Asqrt%28%28x%2By%29%5E2%2A%28x%2By%29%29-5x%5E2%2Asqrt%28x%2By%29 Factor %28x%2By%29%5E3 to get %28x%2By%29%5E2%2A%28x%2By%29


7x%2Asqrt%28%28x%2By%29%5E2%29%2Asqrt%28x%2By%29-5x%5E2%2Asqrt%28x%2By%29 Break up the first root.


7x%2A%28x%2By%29%2Asqrt%28x%2By%29-5x%5E2%2Asqrt%28x%2By%29 Take the square root of %28x%2By%29%5E2 to get x%2By.


Note: since every variable is positive, this means that x%2By is also positive. This allows us to say that sqrt%28%28x%2By%29%5E2%29=x%2By


%287x%2A%28x%2By%29-5x%5E2%29sqrt%28x%2By%29 Factor out the GCF sqrt%28x%2By%29


%287x%5E2%2B7xy-5x%5E2%29sqrt%28x%2By%29 Distribute.


So