# Simplify the following expression using Boolean Algebra into sum-of-products (SOP) expressions

Simplify the following expression using Boolean Algebra into sum-of-products (SOP) expressions $Q.S.U + (Q' + S').(R + V) + U.(R + V) + Q' + S.T.U$

$.$ = AND

$+$ = OR

This is what I have so far

$Q.S.U + (Q' + S').(R + V) + U.(R + V) + Q' + S.T.U$

= $Q.S.U + Q'.(R+V) + S'.(R+V) + R.U + U.V + Q' + S.T.U$

= $Q.S.U + Q'.R + Q'.V + S'.R + S'.V + R.U + U.V + Q' + S.T.U$

Are there any more ways to simplify this expression?

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Is $Q'$ the negative of $Q$ ? In this case note that $Q'+QSU=Q'+SU$ and $Q'+Q'R = Q'$. –  user10676 Apr 25 '13 at 16:23

Q'  + S U  + S' R  + S' V