Question 608140


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



Now let's FOIL the expression.



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



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



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



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



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



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So we have the terms: {{{x^2}}}, {{{-y*x}}}, {{{3*y*x}}}, {{{-3*y^2}}} 



{{{x^2-y*x+3*y*x-3*y^2}}} Now add every term listed above to make a single expression.



{{{x^2+2yx-3y^2}}} Now combine like terms.



So {{{(x+3y)(x-y)}}} FOILs to {{{x^2+2yx-3y^2}}}.



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


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