SOLUTION: {{{(6+sqrt(-3))(2-sqrt(-6))}}} Perform the operation and write the result in standard form

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Question 217286: %286%2Bsqrt%28-3%29%29%282-sqrt%28-6%29%29

Perform the operation and write the result in standard form
Answer by drj(1380) About Me  (Show Source):
You can put this solution on YOUR website!
%286%2Bsqrt%28-3%29%29%282-sqrt%28-6%29%29

Perform the operation and write the result in standard form.

Step 1. You can use FOIL to multiply the terms:

%286%2Bsqrt%28-3%29%29%282-sqrt%28-6%29%29=6%2A2-6%2Asqrt%28-6%29%2B2%2Asqrt%28-3%29-sqrt%28-3%29%2Asqrt%28-6%29


%286%2Bsqrt%28-3%29%29%282-sqrt%28-6%29%29=12-6sqrt%28-6%29%2B2sqrt%28-3%29-sqrt%28-3%29%2Asqrt%28-6%29

Step 2. Replace sqrt%28-3%29=sqrt%28-1%29%2Asqrt%283%29=i%2Asqrt%283%29 and sqrt%28-6%29=sqrt%28-1%29%2Asqrt%286%29=i%2Asqrt%286%29 where i=sqrt%28-1%29

Also, sqrt%28-3%29%2Asqrt%28-6%29=i%2Asqrt%283%29%2Ai%2Asqrt%286%29=-1%2Asqrt%2818%29=-3%2Asqrt%282%29 and i%5E2=-1

Step 3. Substitute results in Step 2 into Step 1.

12-6sqrt%28-6%29%2B2sqrt%28-3%29-sqrt%28-3%29%2Asqrt%28-6%29=12-6%2Ai%2Asqrt%286%29%2B2%2Ai%2Asqrt%283%29-%28-3%29sqrt%282%29

12-6sqrt%28-6%29%2B2sqrt%28-3%29-sqrt%28-3%29%2Asqrt%28-6%29=%2812%2B3sqrt%282%29%29%2Bi%2A%282sqrt%283%29-6sqrt%286%29%29


Step 4. ANSWER: %286%2Bsqrt%28-3%29%29%282-sqrt%28-6%29%29=%2812%2B3sqrt%282%29%29%2Bi%2A%282sqrt%283%29-6sqrt%286%29%29



I hope the above steps and explanation were helpful.

For Step-By-Step videos on Introduction to Algebra,
please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra and
for Trigonmetry please visit
http://www.FreedomUniversity.TV/courses/Trigonometry.

Also, good luck in your studies and contact me at
john@e-liteworks.com for your future math needs.

Respectfully,
Dr J