can someone tell me how 2x3+ 3squared + 2x3squared + 1 is 7+3x3squared? the only part i dont understand is where my book got the 3 from i thought it should be 7+2x3squared?
All they are doing is pretty much using the FOIL method, first let $\displaystyle x = \sqrt3 $
$\displaystyle (\sqrt3 + 1)(2\sqrt3 + 1)$
This can be re written as : $\displaystyle (x + 1)(2x + 1)$ by filling in x's for all square root 3's. now just FOIL that and you will get: $\displaystyle 2x^2 + x + 2x + 1$ combine like terms giving you: $\displaystyle 2x^2 + 3x + 1$ now fill in $\displaystyle \sqrt3$ for all the x's which gives you $\displaystyle 2(\sqrt3)^2 + 3\sqrt3 + 1$ Then once you simplify that, you get $\displaystyle 2(3) + 3\sqrt3 + 1 = 7 + 3\sqrt3$