Question

Rút gọn các biểu thức sau

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

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

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

Answer 1

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

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

= a + b

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

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

Answer 2

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

       \(=a-b+a+b-c-a+b+c\)

       \(=a+b\)

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

       \(=a-b-b+c+c-a-a+b+c\)

       \(=-a-b+3c\)

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

      \(=-a+b+c-a+b-c+a-b+c\)

      \(=-a+b+c\)

Answer 3

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

   =a-b+a+b-c-a+b+c

   =a+(-b)+a+b+(-c)+(-a)+b+c

   =a+b

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

   =a+b-b+c+c-a+a-b+c

   =a+b+(-b)+c+c+(-a)+a+(-b)+c

   =a+(-b)+3c

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

   =-a+b+c-a+b-c+a-b+c

   =-a+b+c+(-a)+b+(-c)+a+(-b)+c

   =-a+b+c