Question

Chứng minh đẳng thức sau:

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

Answer 1

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

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

= 0+0-b-d

= -(b+d) (ĐPCM)

Answer 2

Ta có:

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

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

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

\(=0+0-b-d\)

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

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

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

Answer 3

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

Ta chuyển vế bên trái:

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

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

=-(b+d)+0+0

=-(b+d)+0

=-(b+d)