Question 542175


{{{(1+2t)(1-3t^2)}}} Start with the given expression.



Now let's FOIL the expression.



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



{{{(highlight(1)+2t)(highlight(1)-3t^2)}}} Multiply the <font color="red">F</font>irst terms:{{{(1)*(1)=1}}}.



{{{(highlight(1)+2t)(1+highlight(-3t^2))}}} Multiply the <font color="red">O</font>uter terms:{{{(1)*(-3*t^2)=-3*t^2}}}.



{{{(1+highlight(2t))(highlight(1)-3t^2)}}} Multiply the <font color="red">I</font>nner terms:{{{(2*t)*(1)=2*t}}}.



{{{(1+highlight(2t))(1+highlight(-3t^2))}}} Multiply the <font color="red">L</font>ast terms:{{{(2*t)*(-3*t^2)=-6*t^3}}}.



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So we have the terms: {{{1}}}, {{{-3*t^2}}}, {{{2*t}}}, {{{-6*t^3}}} 



{{{1-3*t^2+2*t-6*t^3}}} Now add every term listed above to make a single expression.



{{{1-3t^2+2t-6t^3}}} Now combine like terms.



So {{{(1+2t)(1-3t^2)}}} FOILs to {{{1-3t^2+2t-6t^3}}}.



In other words, {{{(1+2t)(1-3t^2)=1-3t^2+2t-6t^3}}}.



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