Question 147513


{{{(a-3b)^2 }}} Start with the given expression.



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



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



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



{{{(a+highlight(-3b))(a+highlight(-3b))}}} Multiply the <font color="red">L</font>ast terms:{{{(-3*b)*(-3*b)=9*b^2}}}.



{{{a^2-3*a*b-3*a*b+9*b^2}}} Now collect every term to make a single expression.



{{{a^2-6*a*b+9*b^2}}} Now combine like terms.



So {{{(a-3b)^2 }}} FOILS to {{{a^2-6*a*b+9*b^2}}}.



In other words, {{{(a-3b)^2 =a^2-6*a*b+9*b^2}}}.