Question

Chứng minh đẳng thức:

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

B) (a + b) - (b - a) + c = 2a + c 

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

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

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

        Giúp mk nha,mk cảm ơn nhiều ,cố gắng giúp mk nha.Thank.

 

Answer 1

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)