Product of two negative numbers is positive
When two numbers multiply, the first number is known as the Multiplicand and the second as the Multiplier. The answer is the Product.
Example
Consider (-a) x (-b)
Add b to the the Multiplier (-b)
then (-a) x (b + (-b)) .................................. (i)
Since b + (-b) = 0
therefore (-a) x (b + (-b)) = 0 .................... (ii)
Apply Distributive Law to (i)
(-a) x (b + (-b)) = (-a) x b + (-a) x (-b) ..... (iii)
Substitute (ii) into the LHS of (iii),
then 0 = (-a) x (b) + (-a) x (-b) ................. (iv)
Because (-a) x (b) = - (a) x (b) ................. (v)
Substitute (v) into (iv)
then - (a) x (b) + (-a) x (-b) = 0 ............... (vi)
Add (a) x (b) on both sides of (vi)
then - (a) x (b) + (a) x (b) + (-a) x (-b) = (a) x (b)
therefore (-a) x (-b) = (a) x (b)
This proves that Multiplying two negative numbers gives a positive answer.
QED.
