Question

prove that (-a)(-b) = ab​

Answer 1

Theorem

For any a, b, (-a)(-b) = ab

Proof

By the first corollary in the previous theorem, -a = (-1)a and -b = (-1)b. Using the Commutative Axiom of Multiplication (Axiom 3M) and the associative axiom (Axiom 2M) several times, results to

(-a)(-b) = (-1)(a)(-1)(-b) = (-1)(-1)(a)(b).

By the second corollary in the previous theorem, we have

(-1)(-1)(a)(b) = ab.

Answer 2

Step-by-step explanation:

Prove

(-a)(-b) = ab

As we know

(-)(-)=(+)

(-)(+)=(-)

(+)(-)=(-)

(+)(+)=(+)

As it is in the formula of (-)(-)=(+)

Hence the answer would be (-a)(-b)=ab

HENCE PROVED