Question 197993
{{{(x+y)^2}}} Start with the given expression.



{{{(x+y)(x+y)}}} Expand. Remember something like {{{x^2=xx}}}.



Now let's FOIL the expression.



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



{{{(highlight(x)+y)(highlight(x)+y)}}} Multiply the <font color="red">F</font>irst terms:{{{(x)(x)=x^2}}}.



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



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



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



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So we have the terms: {{{x^2}}}, {{{xy}}}, {{{xy}}}, {{{y^2}}} 



{{{x^2+xy+xy+y^2}}} Now add every term listed above to make a single expression.



{{{x^2+2xy+y^2}}} Now combine like terms.



So {{{(x+y)^2}}} FOILs to {{{x^2+2xy+y^2}}}.



In other words, {{{(x+y)^2=x^2+2xy+y^2}}}.