prove that for any real number and b, a(-b)=-(ab)?

Answer 1

This is an example of the Distributive Property of Multiplication.

a(-b) = a*-1*b = -1*a*b = -1*b*a = b*a*-1 in whatever order.
Because -1*a = -a, the expression may also be written as -a*b or -ab.

Answer 2

I assume you mean a and b are real numbers.
Then ab = real number by the closure property
So -ab is a real number s is a(-b) = -ab

Answer 3

distribute a(-b) = (-b * a) = -(ab) remember, multiplication is communitive, and you may placed the minus sign everywhere you like as lengthy because of the fact the only issues happening are multiplication or branch