Question 334575


{{{(2n-5)(3n-1)}}} Start with the given expression.



Now let's FOIL the expression.



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



{{{(highlight(2n)-5)(highlight(3n)-1)}}} Multiply the <font color="red">F</font>irst terms:{{{(2*n)*(3*n)=6*n^2}}}.



{{{(highlight(2n)-5)(3n+highlight(-1))}}} Multiply the <font color="red">O</font>uter terms:{{{(2*n)*(-1)=-2*n}}}.



{{{(2n+highlight(-5))(highlight(3n)-1)}}} Multiply the <font color="red">I</font>nner terms:{{{(-5)*(3*n)=-15*n}}}.



{{{(2n+highlight(-5))(3n+highlight(-1))}}} Multiply the <font color="red">L</font>ast terms:{{{(-5)*(-1)=5}}}.



{{{6*n^2-2*n-15*n+5}}} Now collect every term to make a single expression.



{{{6*n^2-17*n+5}}} Now combine like terms.



So {{{(2n-5)(3n-1)}}} FOILs to {{{6*n^2-17*n+5}}}.



In other words, {{{(2n-5)(3n-1)=6*n^2-17*n+5}}}.



So the trinomial that represents the area is {{{6*n^2-17*n+5}}}