Question

Bài 1: Chứng tỏ

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

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

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

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

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

Answer 1

Bai 1 :

a, Ta có : \(\left(a-b+c\right)-\left(a+c\right)=a-b+c-a-c=-b\) ( đpcm )

b, Ta có : \(\left(a+b\right)-\left(b-a\right)+c=a+b-b+a+c=2a+c\) (đpcm)

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

= \(-2b\) ( đpcm )

d, Ta có : \(a\left(b+c\right)-a\left(b+d\right)=ab+ac-ab-ad\)

= \(ac-ad=a\left(c-d\right)\) ( đpcm )

e, Ta có : \(a\left(b-c\right)+a\left(d+c\right)=ab-ac+ad+ac\)

= \(ab+ad=a\left(b+d\right)\) ( đpcm )