Question

rút gọn:

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

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

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

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

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

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

Answer 1

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

b. \(-\left(a-c\right)-\left(a-b+c\right)=-a-c-a+b-c=b-2a-2c\)

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

d.\(-\left(a-b+c\right)-\left(a+b+c\right)=-a+b-c-a-b-c=-2a-2c=-2\left(a+c\right)\)e. \(\left(a+b\right)-\left(a-b\right)+\left(a-c\right)-\left(a+c\right)=a+b-a+b+a-c-a-c=2b-2c=2\left(b-c\right)\)

f. \(\left(a+b-c\right)+\left(a-b+c\right)-\left(b+c-a\right)-\left(a-b-c\right)=a+b-c+a-b+c-b-c+a-a+b+c=2a\)

Answer 2

a) -a - (b - a - c)

= -a - b + a + c

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

= 0 - (b + c)

= -(b + c)

d) -(a - b + c) - (a + b + c)

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

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

= (-a - a) + 0 + 0

= -a - a

e) (a + b) - (a - b) + (a - c) - (a + c)

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

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

= 0 + 2a + 2b - 0

= 2a + 2b

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

= -a + c - a + b - c

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

= [(-a) + (-a)] + 0 + b

= 2(-a) + b

c) b - (b + a - c)

= b - b - a + c

= 0 - a - c

= -a - c

f) (a + b - c) + (a - b + c) - (b + c - a) - (a - b - c)

= 0 - (b + c - a) - (a - b - c)

= 0 - b - c + a - a + b - c

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

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

= 0 - 0 + 0

= 0