Question 169711
Let {{{x=sqrt(3)}}} 


So the expression {{{(1+sqrt(3))^2}}} becomes {{{(1+x)^2}}}





{{{(1+x)^2}}} Start with the given expression.



{{{(1+x)(1+x)}}} Expand. Remember something like {{{A^2=A*A}}}.



Now let's FOIL the expression.



Remember, when you FOIL an expression, you follow this procedure:



{{{(highlight(1)+x)(highlight(1)+x)}}} Multiply the <font color="red">F</font>irst terms:{{{(1)*(1)=1}}}.



{{{(highlight(1)+x)(1+highlight(x))}}} Multiply the <font color="red">O</font>uter terms:{{{(1)*(x)=x}}}.



{{{(1+highlight(x))(highlight(1)+x)}}} Multiply the <font color="red">I</font>nner terms:{{{(x)*(1)=x}}}.



{{{(1+highlight(x))(1+highlight(x))}}} Multiply the <font color="red">L</font>ast terms:{{{(x)*(x)=x^2}}}.



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{{{1+x+x+x^2}}} Now collect every term to make a single expression.



{{{1+2*x+x^2}}} Now combine like terms.



So {{{(1+x)^2}}} FOILs to {{{1+2*x+x^2}}}.



In other words, {{{(1+x)^2=1+2*x+x^2}}}.




So {{{(1+sqrt(3))^2=1+2*sqrt(3)+(sqrt(3))^2}}}




{{{1+2*sqrt(3)+(sqrt(3))^2}}} Start with the right side of the last equation



{{{1+2*sqrt(3)+3}}} Square {{{sqrt(3)}}} to get 3



{{{4+2*sqrt(3)}}} Combine like terms.




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Answer:



So {{{(1+sqrt(3))^2=4+2*sqrt(3)}}}