Prove in detail that for any a b c d epsilon R a b b a a

Prove in detail that for any a, b, c, d, epsilon R -(a - b) = b - a (a - b)(c - d) = (ac + bd) - (ad + bc)

Solution

(a) given that a,b,c,d are any real numbers.

LHS:

-(a-b)=-a-(-b) multiply with \"-1\"

=-a+b

=b-a

=RHS

(b)

LHS:

(a-b)(c-d)=ac-ad-bc+bd using distributive property

=(ac+bd)-ad-bc

=(ac+bd)-(ad+bc)

=RHS