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11 tháng 7 2021

Ta có: a-(b-c)=a-b+c

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

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

Vì a-b+c=a-b+c=a-b+c

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

25 tháng 3 2020

a) a(b-c)+c(a-b)=ab-ac+ca-cb=ab-cb=b(a-c)

b) a(b-c)-b(a+c)=ab-ac-ab-bc=-ac-bc=-c(a+b)

c) a(b+c)-b(a-c)=ab+ac-ab+bc=ac+bc=c(a+b)

d) a(b-c)-a(b+d)=ab-ac-ab-ad=-ac-ad=-a(a+d)

25 tháng 3 2020

a) a(b - c) + c(a - b) = ab - ac + ac - bc = ab - bc = b(a - c)

b) a(b - c) - b(a + c) = ab - ac - ab - bc = -ac - bc = (a + b). (-c)

c) a(b + c) - b(a - c) = ab + ac - ab + bc = ac + bc = (a + b)c

d) a(b - c) - a(b + d) = ab - ac - ab - ad = -ac - ad = -a(c + d)

7 tháng 1 2018

a)-b+c

d)-2a-2c

e)2b-2c

b)-2a+b

c)-a+c

f)a

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

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

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

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

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

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

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

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

\(\Rightarrow VT=VP\left(đpcm\right)\)

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

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

\(\Rightarrow VT=VP\left(đpcm\right)\)

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

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

\(\Rightarrowđpcm\)

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

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

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

\(\Rightarrow VT=VP\left(đpcm\right)\)

e, \(-\left(-a+b+c\right)+\left(b+c-1\right)=\left(b-c+6\right)-\left(7-a+b\right)+c\)

\(a-b-c+b+c-1=b-c+6-7+a-b+c\)

\(a-1=-1+a\Rightarrow a-1=a+\left(-1\right)\Rightarrow a-1=a-1\)

\(\Rightarrow VT=VP\left(đpcm\right)\)

18 tháng 3 2020

\( a)\left( {a + b - c} \right) + \left( {b + c - a} \right) + \left( {a + c - b} \right)\\ = a + b - c + b + c - a + a + c - b\\ = a + b + c\\ b)\left( {a - b} \right) + \left( {b - c + a} \right) + \left( {c - b} \right)\\ = a - b + b - c + a + c - b\\ = 2a + b\\ c)\left( {2a - b + c} \right) + \left( {b - c + a} \right) + \left( {c - 2a + b} \right)\\ = 2a - b + c + b - c + a + c - 2a + b\\ = a + b + c\\ d)\left( {a - c + b} \right) + \left( {b - c - a} \right) - a - b - c\\ = a - c + b + b - c - a - a - b - c\\ = - a - b - 3c \)

18 tháng 3 2020

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

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

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

= a + b + c

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

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

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

= 2a - b

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

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

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

= b + c

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

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

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

= b - 2a - 3c

Chúc bạn học tốt@@

7 tháng 1 2018

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

7 tháng 1 2018

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

3 tháng 2 2021

\(\text{ (a-b+c)-(a+c)}=a-b+c-a-c=\left(a-a\right)-b+\left(c-c\right)=-b\)

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

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

\(a\left(b+c\right)-a\left(b+d\right)=ab+ac-ab+ad=ac+ad=a\left(c+d\right)\)

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

3 tháng 2 2021

Cảm ơn nhiều :)))

7 tháng 12 2017

Ta có:

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

=a+b

B=a-b-b+c+c-a-a+b+c=3c-a-b

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

4 tháng 1 2017

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

= a + c - a + b - c

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

= 0 + 0 + b

= b

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

= -a - b + a + c + b

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

= 0 + 2b + c

= 2b + c

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

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

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

= 0 + 0 + 0

= 0

d) (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 + 2b + 2c

= 2b + 2c

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

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

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

= 2a + 0 + 2c

= 2a + 2c