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

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

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

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

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

3,-(a+b-c)+(a-b-c)

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

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

=0-b-b+0

=-b-b

=-2b(đpcm)

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

=ab+ac-ab+ad

=(ab-ab)+ac+ad

=0+ac+ad

=ac+ad

=a(c+d)(đpcm)

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

=ab-ac+ad+ac

=(-ac+ac)+ab+ad

=0+ab+ad

=ab+ad

=a(b+d)(đpcm)

k cho mình vs

1. ( a - b + c ) - ( a + c ) = - b

Ta có : VT = ( a - b + c ) - ( a + c )

                = a - b + c - a - c

                = - b = VP

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

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

Ta có : VT = ( a + b ) - ( b - a ) + c

                = a + b - b + a + c

                = 2a + c = VP  

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

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

Ta có : VT = - ( a + b - c ) + ( a - b - c )

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

                = - 2b = VP 

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

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

Ta có : VT = a ( b + c ) - a ( b + d )

                = ab + ac - ab  - ad 

                = ac - ad

                = a ( c - d ) = VP 

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

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

Ta có : VT = a( b - c ) + a ( d + c )

                = a ( b - c + d + c )

                = a( b + d ) = VP

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

VT là vế trái 

VP là vế phải .

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

=a+b-b+a+c

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

=2a+0+c

=2a+c(đpcm)

Ta có \(\frac{2a+b+c+d}{a}=\frac{a+2b+c+d}{b}=\frac{a+b+2c+d}{c}=\frac{a+b+c+2d}{d}\)

=> \(1+\frac{a+b+c+d}{a}=1+\frac{a+b+c+d}{b}=1+\frac{a+b+c+d}{c}=1+\frac{a+b+c+d}{d}\)

=> \(\frac{a+b+c+d}{a}=\frac{a+b+c+d}{b}=\frac{a+b+c+d}{c}=\frac{a+b+c+d}{d}\)

Khi a + b + c + d => a + b = -(c + d) ; 

b + c = -(a + d) ; 

c + d = -(a + b) 

d + a = -(b + c)

Khi đó \(M=\frac{-\left(c+d\right)}{c+d}+\frac{-\left(a+d\right)}{a+d}+\frac{-\left(a+b\right)}{a+b}+\frac{-\left(b+c\right)}{b+c}\)

= (-1) + (-1) + (-1) + (-1) = -4

Khi a + b + c + d \(\ne0\)

=> \(\frac{1}{a}=\frac{1}{b}=\frac{1}{c}=\frac{1}{d}\Rightarrow a=b=c=d\)

Khi đó M = \(\frac{2a}{2a}+\frac{2b}{2b}+\frac{2c}{2c}+\frac{2d}{2d}=2+2+2+2=8\)

Vậy khi a + b + c + d = 0 thì M = -4

khi a + b + c + d \(\ne\)0 thì M = 8

thanks bn nha!!!!!!!!!!!!

1,( a + b ) - ( b - a) +c 

= a + b - b + a + c

= ( a + a )  + ( b - b ) + c

= 2a + c

2. - ( a + b - c) + ( a - b - c ) 

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

= ( -a  + a ) - ( b + b ) + ( c - c )

= -2b

mấy câu sau bn tự giải nhá. MỆT

Mấy bài này bỏ ngoặc rồi rút gọn là ra thôi

1,a-b+c-a-c=-b

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

3,-a-b+c+a-b-c=-2b

4,ab+ac-ab-ad=ac-ad=a(c-d)

5,ab-ac+ad+ac=ab+ad=a(b+d)

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

2)(a+b)-(b-a)=2a+c=a+b-b+c+c=2c+a(ko the bang 2a+c)

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

tk minh nha

lam dc the thoi

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

<=>a-b+c-a-c=-b

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

<=>0+0-b=-b

<=>-b=-b

Vậy (a-b+c)-(a+c)=-b

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

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

<=>a+a+c=2a+c

<=>2a+c=2a+c

Vậy (a+b)-(b-a)+c=2a+c

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

<=>-a-b+c+a-b-c=-2b

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

<=>0+0-2b=-2b

<=>-2b=-2b

Vậy -(a+b-c)+(a-b-c)=-2b

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

<=>ab+ac-ab-ad=a(c-d)

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

<=>a(c-d)=a(c-d)

Vậy a(b+c)-a(b+d)=a(c-d)

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

<=>ab-ac+ac+ad=a(b+d)

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

<=>a(b+d)=a(b+d)

Vậy a(b-c)+a(c+d)=a(b+d)