Question 198861
First, let's FOIL {{{(3x+3y)^2}}}



{{{(3x+3y)^2}}} Start with the given expression.



{{{(3x+3y)(3x+3y)}}} Expand. Remember something like {{{x^2=x*x}}}.



Now let's FOIL the expression.



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



{{{(highlight(3x)+3y)(highlight(3x)+3y)}}} Multiply the <font color="red">F</font>irst terms:{{{(3*x)*(3*x)=9*x^2}}}.



{{{(highlight(3x)+3y)(3x+highlight(3y))}}} Multiply the <font color="red">O</font>uter terms:{{{(3*x)*(3*y)=9*x*y}}}.



{{{(3x+highlight(3y))(highlight(3x)+3y)}}} Multiply the <font color="red">I</font>nner terms:{{{(3*y)*(3*x)=9*x*y}}}.



{{{(3x+highlight(3y))(3x+highlight(3y))}}} Multiply the <font color="red">L</font>ast terms:{{{(3*y)*(3*y)=9*y^2}}}.



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So we have the terms: {{{9*x^2}}}, {{{9*x*y}}}, {{{9*x*y}}}, {{{9*y^2}}} 



{{{9*x^2+9*x*y+9*x*y+9*y^2}}} Now add every term listed above to make a single expression.



{{{9*x^2+18*x*y+9*y^2}}} Now combine like terms.



So {{{(3x+3y)^2}}} FOILs to {{{9*x^2+18*x*y+9*y^2}}}.



In other words, {{{(3x+3y)^2=9*x^2+18*x*y+9*y^2}}}.



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So {{{(3x+3y)^2(2x+3y)}}} becomes {{{(9x^2+18xy+9y^2)(2x+3y)}}}




{{{(9x^2+18xy+9y^2)(2x+3y)}}} Start with the given expression.



{{{(2x+3y)(9x^2+18xy+9y^2)}}} Rearrange the terms.



{{{2x(9x^2+18xy+9y^2)+3y(9x^2+18xy+9y^2)}}} Expand



{{{2x(9x^2)+2x(18xy)+2x(9y^2)+3y(9x^2)+3y(18xy)+3y(9y^2)}}} Distribute



{{{18x^3+36x^2*y+18x*y^2+27x^2*y+54x*y^2+27y^3}}} Multiply



{{{18x^3+63x^2*y+72x*y^2+27y^3}}} Combine like terms.



So {{{(3x+3y)^2*(2x+3y)=18x^3+63x^2*y+72x*y^2+27y^3}}}