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A+A*b does not mean A plus Ab
the operation signified by "+" is called "or"
the operation signified by "*" is called "and"
there are four possible outcomes of a+a*b
if a=1 and b=1 the result is 1
if a=1 and b=0 the result is 1
if a=0 and b=1 the result is 0
if a=0 and b=0 the result is 0
a+a*b is 1 if a is 1 and a+a*b is 0 if a is 0 regardless of the value of b
thus a+a*b=a
Q.E.D.
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