Question 242940
You could use the difference of squares formula, but let's do it the long way.





{{{(x*y+a*b^2)(x*y-a*b^2)}}} Start with the given expression.



Now let's FOIL the expression.



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



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



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



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



{{{(x*y+highlight(a*b^2))(x*y+highlight(-a*b^2))}}} Multiply the <font color="red">L</font>ast terms:{{{(a*b^2)*(-a*b^2)=-a^2*b^4}}}.



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So we have the terms: {{{x^2*y^2}}}, {{{-x*y*a*b^2}}}, {{{x*y*a*b^2}}}, and {{{-a^2*b^4}}} 



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



{{{x^2*y^2-a^2*b^4}}} Now combine like terms.



So {{{(x*y+a*b^2)(x*y-a*b^2)}}} FOILs to {{{x^2*y^2-a^2*b^4}}}.



In other words, {{{(x*y+a*b^2)(x*y-a*b^2)=x^2*y^2-a^2*b^4}}}.




Note: recall that the difference of squares formula is {{{(A+B)(A-B)=A^2-B^2}}}. So you could have used this formula where in this case {{{A=xy}}} and {{{B=ab^2}}}