Question

For the following values of A,B, and C, verify that A*(B+C) = A*B+A*C
a. A= 1/2 B= 2/3 C= 3/7
b.A=-2/3 B= -3/4 C=1/5

Answer 1

In situtation A

A=1/2 B=2/3 C=3/7

then L.H.S=A(B+C)=1/2(2/3+3/7)

=1/2(23/21)

=23/42..

R.H.S.=A*B+A*C

= 1/2*2/3+1/2*3/7

=1/3+3/14

=23/42

Now in situation B,

A=-2/3 B=-3/4 C=1/5

Then,

L.H.S.=A(B+C)

=-2/3(-3/4+1/5)

=-2/3(-11/20)

=11/30

R.H.S=A*B+A*C

=-2/3*-3/4+(-2/3*1/5)

=1/2-2/15

=11/30

since, L.H.S=R.H.S

hence. proved