Question

Rút gọn các biểu thức sau :

a) \(A=\left(a-b\right)+\left(a+b-c\right)-\left(a-b-c\right)\)

b) \(B=\left(a-b\right)-\left(b-c\right)+\left(c-a\right)-\left(a-b-c\right)\)

c) \(C=\left(-a+b+c\right)-\left(a-b+c\right)-\left(-a+b-c\right)\)

Answer 1

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

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

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

=a+b

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

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

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

=-a-b+3c

c. 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+c

Answer 2

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

      = a-b+a+b-c-a+b+c

      = ( a +a -a) -( b-b-b) - (c-c)

      =  a - (-b) - 0

      = a +b

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

      = a - b - b +c +c - a - a +b +c

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

      =  - a - b + 3c

c) 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 + c