Question

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

\(\text{ (a-b+c)-(a+c)}=a-b+c-a-c=\left(a-a\right)-b+\left(c-c\right)=-b\)

\(\left(a+b\right)-\left(b-a\right)+c=a+b-b+a+c=2a+c\)

\(-\left(a+b-c\right)+\left(a-b-c\right)=-a-b+c+a-b-c=-2b\)

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

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