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b*ab = ab2

Suppose b*ab = ab + b2. Assume a and b are non-zero integers. Then

ab2 = ab + b2

b = 1 + b/a would have to be true for all b.

Counter-example:

b = 2; a = 3

b(ab) = 2(3)(2) = 12 = ab2 = (4)(3)

ab + b2 = (2)(3) + (2) = 10

but 10 does not = 12. Contradiction. So it cannot be the case that b = 1 + b/a is true for all b and, therefore, b*ab does not = ab + b2

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13y ago

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