How do you multiply #(x y - 3) ( x y + 3)#?

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Answer 1 · 2017-07-11T00:56:47

#(xy-3)(xy+3)=x^2y^2-9#

We can apply the F.O.I.L method.

If you are not already familiar, F.O.I.L stands for First, Outside, inside, Last

We begin by multiplying the first terms in each parenthesis.

#(color(red)(xy)-3)(color(red)(xy)+3) = x^2y^2#

Next we multiply the outside terms:

#(color(red)(xy)-3)(xy+color(red)(3))=3xy#

Then the Inside terms:

#(xycolor(red)(-3))(color(red)(xy)+3)=-3xy#

And finally the last terms:

#(xycolor(red)(-3))(xy+color(red)(3))=-9#

We then add all of them up to get the following expression:

#x^2y^2+3xy-3xy-9#

We can simplify this further as the two middle terms cancel and we are left with this.

#x^2y^2-9#