Question 321517
"the product of 3 less than twice x and 2 more than the quantity 3 times x" means that {{{(2x-3)(3x+2)}}}



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



Now let's FOIL the expression.



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



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



{{{(highlight(2x)-3)(3x+highlight(2))}}} Multiply the <font color="red">O</font>uter terms:{{{(2x)*(2)=4x}}}.



{{{(2x+highlight(-3))(highlight(3x)+2)}}} Multiply the <font color="red">I</font>nner terms:{{{(-3)*(3x)=-9x}}}.



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



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So we have the terms: {{{6x^2}}}, {{{4x}}}, {{{-9x}}}, {{{-6}}} 



{{{6x^2+4x-9x-6}}} Now add every term listed above to make a single expression.



{{{6x^2-5x-6}}} Now combine like terms.



So {{{(2x-3)(3x+2)}}} FOILs to {{{6x^2-5x-6}}}.



In other words, {{{(2x-3)(3x+2)=6x^2-5x-6}}}.