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

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}}}```