Question

Chứng minh:

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

2/ - ( -a + c - d ) - ( c - a + d ) = 0

3/ a( b - c - d ) - a( b + c - d ) = 0

Answer 1

1) Xét:

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

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

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

2) Xét:

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

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

\(=0\)

Vậy \(-\left(-a+c-d\right)-\left(-c-a+d\right)=0\)

3) Xét:

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

\(=ab-ac-ad-ab-ac+ad\)

\(=\left(ab-ab\right)+\left(ac-ac\right)+\left(-ad+ad\right)\)

\(=0\)

Vậy \(a\left(b-c-d\right)-a\left(b+c-d\right)=0\)

P/s: test lại đề phần 2) dấu của số trừ