4v3(2v3-v6)
In your problem... I am assuming that the v3 and v6 parts mean the square root of 3 and square root of 6.
This is a straightforward distribution problem. Remembering that vavb = vab (square root of a times the square root of b equals the square root of ab)
4v3(2v3-v6)
So... distributing the 4v3 we get...
8v9 - 4v18 4*2 is 8, v3 times v3 is v9, 4 times -1 is -4 and v3 times v6 is v18
But: the square root of 9 equals 3
8*3 - 4v18 = 24 - 4v18
and now we need to look at v18. We can rewrite this as v9v2. and again, v9 equals 3
So now we get 24 - 4v9v2
= 24 - 4*3v2
= 24 - 12v2
And THAT'S the answer to your question.
4v3(2v3-v6) = 24 - 12v2
