Question

write in the simplest form ="TexFormula1" title=" (2-\sqrt{7} ) (1+2\sqrt{7} ) " alt=" (2-\sqrt{7} ) (1+2\sqrt{7} ) " align="absmiddle" class="latex-formula">

Answer 1

You will FOIL this out to simplify.  First outers, inners last.  2*1 = 2; 2*2sqrt7 = 4sqrt7; -sqrt7*1=-sqrt7; -sqrt7*2sqrt7 = 2sqrt49.  This is what all that looks like: $2+4 \sqrt{7}- \sqrt{7}-2 \sqrt{49}$.  Combining like terms we have $2+3 \sqrt{7} -2 \sqrt{49}$.  The sqrt 49 is equal to 7, so we can continue simplifying: $2+3 \sqrt{7}-2(7)$ which equals $2+3 \sqrt{7}-14$.  Finally, $-12+3 \sqrt{7}$.  Or, putting the positive term first, it would also be correct to write $3 \sqrt{7}-12$