Question 193778


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



Now let's FOIL the expression.



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



{{{(highlight(x^2)+y^2)(highlight(x^2)+y^2)}}} Multiply the <font color="red">F</font>irst terms:{{{(x^2)*(x^2)=x^4}}}.



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



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



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



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So we have the terms: {{{x^4}}}, {{{x^2*y^2}}}, {{{x^2*y^2}}}, and {{{y^4}}} 



{{{x^4+x^2*y^2+x^2*y^2+y^4}}} Now add every term listed above to make a single expression.



{{{x^4+2*x^2*y^2+y^4}}} Now combine like terms.



So {{{(x^2+y^2)(x^2+y^2)}}} FOILs to {{{x^4+2*x^2*y^2+y^4}}}.



In other words, {{{(x^2+y^2)(x^2+y^2)=x^4+2*x^2*y^2+y^4}}}.