Question 124417

{{{(2-9x^3)^2}}} Start with the given expression



{{{(2-9x^3)(2-9x^3)}}} 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(2)-9x^3)(highlight(2)-9x^3)}}} Multiply the First terms:{{{(2)*(2)=4}}}



{{{(highlight(2)-9x^3)(2+highlight(-9x^3))}}} Multiply the Outer terms:{{{(2)*(-9x^3)=-18x^3}}}



{{{(2+highlight(-9x^3))(highlight(2)-9x^3)}}} Multiply the Inner terms:{{{(-9x^3)*(2)=-18x^3}}}



{{{(2+highlight(-9x^3))(2+highlight(-9x^3))}}} Multiply the Last terms:{{{(-9x^3)*(-9x^3)=81x^6}}}



{{{4-18x^3-18x^3+81x^6}}} Now collect every term to make a single expression




{{{-36x^3+81x^6+4}}} Now combine like terms



{{{81x^6-36x^3+4}}} Rearrange the terms in descending order



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Answer:

So {{{(2-9x^3)^2}}} foils and simplifies to  {{{81x^6-36x^3+4}}}


In other words, {{{(2-9x^3)^2=81x^6-36x^3+4}}}