Minimum Sum-Of-Products Expression

Hello,

I am having some difficulty minimizing the following expression:

$\displaystyle f = x_1x_2'x_3' + x_1x_2x_4 + x_1x_2'x_3x_4'$

If I introduce $\displaystyle x_4$ in the first term and $\displaystyle x_3$ in the second term. I must do it in the form $\displaystyle x_3 + x_3'$. That means I create two new expressions and get:

$\displaystyle f = x_1x_2'x_3'x_4 + x_1x_2'x_3'x_4' + x_1x_2x_3x_4 + x_1x_2x_3'x_4 + x_1x_2'x_3x_4'

$

If I combine terms 1 & 2, 2 & 5, 3 & 4 I get:

$\displaystyle f = x_1x_2'x_3' + x_1x_2'x_4' + x_1x_2x_4 $

I am stuck at this point, thanks for any help. I guess the reason I am stuck is that my expression doesn't appear to be minimized all that much from the initial expression. Thanks for any help.