Question 150731


{{{(a+b)^2}}} Start with the given expression.



{{{(a+b)(a+b)}}} Expand. Remember something like {{{x^2=x*x}}}.



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)=a*b}}}.



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



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



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



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



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



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