Given that \(a*b = ab + a + b\) and that \(a ♦ b = a + b = 1\). Find an expression (not involving * or ♦) for (a*b) ♦ (a*c) if a, b, c, are real numbers and the operations on the right are ordinary addition and multiplication of numbers
Soln. a*b = ab + a + b,
a ♦ b = a + b + 1
a*c = ac + a + c
(a*b) ♦ (a*c) = (ab + a + b + ac + a + c + 1)
= ab + ac + 2a + b + c + 1
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