Question 170773

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



Now let's FOIL the expression.



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



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



{{{(highlight(a)+2b)(a+highlight(3b))}}} Multiply the <font color="red">O</font>uter terms:{{{(a)*(3*b)=3*a*b}}}.



{{{(a+highlight(2b))(highlight(a)+3b)}}} Multiply the <font color="red">I</font>nner terms:{{{(2*b)*(a)=2*a*b}}}.



{{{(a+highlight(2b))(a+highlight(3b))}}} Multiply the <font color="red">L</font>ast terms:{{{(2*b)*(3*b)=6*b^2}}}.



---------------------------------------------------



{{{a^2+3*a*b+2*a*b+6*b^2}}} Now collect every term to make a single expression.



{{{a^2+5*a*b+6*b^2}}} Now combine like terms.



So {{{(a+2b)(a+3b)}}} FOILs to {{{a^2+5*a*b+6*b^2}}}.



In other words, {{{(a+2b)(a+3b)=a^2+5*a*b+6*b^2}}}.