Question

 Chứng minh các đẳng thức sau:

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

Answer 1

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

\(=ab-ac-ba-bc+ca-cb=-2bc\)

Answer 2

a(b-c)-b(a+c)+c(a-b)=ab-ab-bc-ac+ac-bc=-2bc

Answer 3

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

\(=ab-ac-ba-bc+ca-cb\)

\(=\left(ab-ba\right)+\left(-ac+ca\right)+\left(-bc-cb\right)\)

\(=0+0-2bc\)

\(=-2bc\)

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

Học tốt

Answer 4

a( b - c ) - b( a + c ) + c( a - b )

= ab - ac - ab - bc + ac - bc

= ( ab - ab ) + ( ac - ac ) + ( -bc - bc )

= -2bc ( đpcm )

Answer 5

                Bài làm :

Ta có :

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

\(=ab-ac-ba-bc+ca-cb\)

\(=\left(ab-ba\right)+\left(-ac+ca\right)+\left(-bc-cb\right)\)

\(=0+0-2bc\)

\(=-2bc\)

=> Điều phải chứng minh