Question 291014
{{{(x-2)^2}}} Start with the given expression



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



{{{(highlight(x)-2)(x+highlight(-2))}}} Multiply the <font color="red">O</font>uter terms:{{{(x)*(-2)=-2x}}}



{{{(x+highlight(-2))(highlight(x)-2)}}} Multiply the <font color="red">I</font>nner terms:{{{(-2)*(x)=-2x}}}



{{{(x+highlight(-2))(x+highlight(-2))}}} Multiply the <font color="red">L</font>ast terms:{{{(-2)*(-2)=4}}}



{{{x^2-2x-2x+4}}} Now collect every term to make a single expression




{{{x^2-4x+4}}} Now combine like terms



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Answer:

So {{{(x-2)^2}}} foils and simplifies to  {{{x^2-4x+4}}}


In other words, {{{(x-2)^2=x^2-4x+4}}}