SOLUTION: (5√6-15√3)(4√6+12√3) Can someone help me with this. The instructions say to simplify. Type an exact answer using radicals as needed.

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: (5√6-15√3)(4√6+12√3) Can someone help me with this. The instructions say to simplify. Type an exact answer using radicals as needed.      Log On


   

Question 374965: (5√6-15√3)(4√6+12√3) Can someone help me with this. The instructions say to simplify. Type an exact answer using radicals as needed.
Found 2 solutions by Fombitz, solver91311:
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Use the FOIL method,

%285%2Asqrt%286%29-15%2Asqrt%283%29%29%2A%284%2Asqrt%286%29%2B12%2Asqrt%283%29%29=120-540

Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!


There are a couple of ways to skin this cat. The first way is just to use FOIL and go at it straight on.



Or notice that the first binomial has a 5 that you can factor out and the second binomial has a 4 that you can factor out:



Now notice that the remaining binomial factors are a conjugate pair, hence the product is the difference of two squares:




John

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