Question

5
Sendo A = a + b - C, B = a - b - c e
C = a - b + c, determine:
a) A - B
b) C - A
c) A - B - C
d) (A + B) - C
e) C - (A + B)
f) B + (A - C)​

Answer 1

Resposta:

Sendo

A = a + b - c

B = a - b - c

C = a - b + c

a) A - B

( a + b - c ) - ( a - b - c ) =

a + b - c - a + b + c =

a - a + b + b - c + c =

2b

b) C - A

( a - b + c ) - ( a + b - c ) =

a - b + c - a - b - c =

a - a - b - b + c - c =

- 2b

c) A - B - C

( a + b - c ) - ( a - b - c ) - ( a - b + c )=

a + b - c - a + b + c - a + b - c =

a - a - a + b + b + b - c + c - c =

- a + 3b - c =

d) (A + B) - C

( a + b - c ) + ( a - b - c ) - ( a - b + c ) =

a + b - c + a - b - c - a - b - c =

a + a - a + b - b - b - c - c - c =

a - b - 3c

e) C - (A + B)

a - b + c - ( ( a + b - c ) + ( a - b - c ) ) =

a - b + c - ( a + b - c + a - b - c) =

a - b + c - ( a + a + b - b - c - c ) =

a - b + c - ( 2a - 2c ) =

a - b + c - 2a + 2c =

3a - b + 3c

f) B + (A - C)

a - b - c + ( a + b - c - ( a - b + c ) ) =

a - b - c + ( a + b - c - a + b - c ) =

a - b - c + ( a - a + b + b - c - c ) =

a - b - c + ( 2b - 2c ) =

a - b - c + 2b - 2c =

a - b - 3c