Question 182046
{{{(x+y)^3}}} Start with the given expression.



{{{(x+y)(x+y)(x+y)}}} Expand. Remember something like {{{A^3}}} expands to {{{A^3=A*A*A}}}



Now let's FOIL the first two "x+y" terms:


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



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)=x*y}}}.



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



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



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



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



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



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



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So this means that {{{(x+y)(x+y)(x+y)}}} then becomes {{{(x^2+2xy+y^2)(x+y)}}}



{{{(x+y)(x^2+2xy+y^2)}}} Rearrange the terms.



{{{x(x^2+2xy+y^2)+y(x^2+2xy+y^2)}}} Expand. Note: {{{(A+B)(C+D+E)=A(C+D+E)+B(C+D+E)}}}



{{{(x)*(x^2)+(x)*(2xy)+(x)*(y^2)+(y)*(x^2)+(y)*(2xy)+(y)*(y^2)}}} Distribute.



{{{x^3+2x^2*y+xy^2+x^2*y+2xy^2+y^3}}} Multiply.



{{{x^3+3x^2y+3xy^2+y^3}}} Now combine like terms.



 So {{{(x+y)(x^2+2xy+y^2)}}} expands to {{{x^3+3x^2y+3xy^2+y^3}}}.



In other words, {{{(x+y)(x^2+2xy+y^2)=x^3+3x^2y+3xy^2+y^3}}}.



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Answer:



So {{{(x+y)^3=x^3+3x^2y+3xy^2+y^3}}}