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.Com
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) (Show Source): You can put this solution on YOUR website!
Use the FOIL method,
Answer by solver91311(24713) (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.
\left(4\sqrt{6}\ -\ 12\sqrt{3}\right)\ =\ 20\,\cdot\,6\ +\ 60\sqrt{18}\ -\ 60\sqrt{18}\ -\ 180\,\cdot\,3\ =\ -420)
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:
\,\cdot\,4\,\cdot\,\left(\sqrt{6}\ -\ 3\sqrt{3}\right))
Now notice that the remaining binomial factors are a conjugate pair, hence the product is the difference of two squares:
\left(\sqrt{6}\ +\ 3\sqrt{3}\right)\ =\ 20\ \cdot\ (6\ -\ 27)\ =\ -420)
John
My calculator said it, I believe it, that settles it
