Question 376624

{{{(15y+20)(15y+21)}}} Start with the given expression.



Now let's FOIL the expression.



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



{{{(highlight(15y)+20)(highlight(15y)+21)}}} Multiply the <font color="red">F</font>irst terms:{{{(15*y)*(15*y)=225*y^2}}}.



{{{(highlight(15y)+20)(15y+highlight(21))}}} Multiply the <font color="red">O</font>uter terms:{{{(15*y)*(21)=315*y}}}.



{{{(15y+highlight(20))(highlight(15y)+21)}}} Multiply the <font color="red">I</font>nner terms:{{{(20)*(15*y)=300*y}}}.



{{{(15y+highlight(20))(15y+highlight(21))}}} Multiply the <font color="red">L</font>ast terms:{{{(20)*(21)=420}}}.



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So we have the terms: {{{225*y^2}}}, {{{315*y}}}, {{{300*y}}}, {{{420}}} 



{{{225*y^2+315*y+300*y+420}}} Now add every term listed above to make a single expression.



{{{225*y^2+615*y+420}}} Now combine like terms.



So {{{(15y+20)(15y+21)}}} FOILs to {{{225*y^2+615*y+420}}}.



In other words, {{{(15y+20)(15y+21)=225*y^2+615*y+420}}}.



Now because the number 3 is the GCF of all the terms, this means that the GCF is 3.



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