Question 257289
# 1


If it's {{{(ab)(ab)}}}, then {{{(ab)(ab)=(a*a)(b*b)=a^2b^2}}}.



If it's {{{(a+b)(a+b)}}}, then...



{{{(a+b)(a+b)}}} Start with the given expression.



Now let's FOIL the expression.



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



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



{{{(highlight(a)+b)(a+highlight(b))}}} Multiply the <font color="red">O</font>uter terms:{{{(a)(b)=ab}}}.



{{{(a+highlight(b))(highlight(a)+b)}}} Multiply the <font color="red">I</font>nner terms:{{{(b)(a)=ab}}}.



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



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So we have the terms: {{{a^2}}}, {{{ab}}}, {{{ab}}}, and {{{b^2}}} 



{{{a^2+ab+ab+b^2}}} Now add every term listed above to make a single expression.



{{{a^2+2ab+b^2}}} Now combine like terms.



So {{{(a+b)(a+b)}}} FOILs to {{{a^2+2ab+b^2}}}.



In other words, {{{(a+b)(a+b)=a^2+2ab+b^2}}}.


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# 2






{{{(y-6)(y+3)}}} Start with the given expression.



Now let's FOIL the expression.



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



{{{(highlight(y)-6)(highlight(y)+3)}}} Multiply the <font color="red">F</font>irst terms:{{{(y)(y)=y^2}}}.



{{{(highlight(y)-6)(y+highlight(3))}}} Multiply the <font color="red">O</font>uter terms:{{{(y)(3)=3y}}}.



{{{(y+highlight(-6))(highlight(y)+3)}}} Multiply the <font color="red">I</font>nner terms:{{{(-6)(y)=-6y}}}.



{{{(y+highlight(-6))(y+highlight(3))}}} Multiply the <font color="red">L</font>ast terms:{{{(-6)(3)=-18}}}.



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So we have the terms: {{{y^2}}}, {{{3y}}}, {{{-6y}}}, {{{-18}}} 



{{{y^2+3y-6y-18}}} Now add every term listed above to make a single expression.



{{{y^2-3y-18}}} Now combine like terms.



So {{{(y-6)(y+3)}}} FOILs to {{{y^2-3y-18}}}.



In other words, {{{(y-6)(y+3)=y^2-3y-18}}}.



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# 3


{{{A=LW}}} Start with the area equation.



{{{A=9x(3x^2+2)}}} Plug in the given length and width.



{{{A=9x(3x^2)+9x(2)}}} Distribute



{{{A=27x^3+18x}}} Multiply



So the area is {{{27x^3+18x}}} square units.