Question

Chứng minh đẳng thức:

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

Answer 1

 -a.(c-d)-d.(a+c)

=-a.c+a.d-d.a-d.c

=(a.d-a.d)-a.c-d.c

=0-(a.c+d.c)

=-(a.c+d.c)

=-[c.(a+d)]

=-c.(a+d)

Answer 2

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

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

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

\(=0-\left(a.c-d.c\right)\)

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

\(=-c.\left(a+d\right)\)( đpcm )

Answer 3

Ta có: VT=-a(c-d)-d(a+c)

=-ac+ad-ad-dc

=-ac-dc

=-c(a+d) =VP
=> đpcm