Question

Chứng minh đẳng thức

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

Answer 1

Có: Vế trái : (a - c)(b + d) - (a - d)(b + c) 

= ab + ad - bc - cd - ab - ac + bd + cd

= ad - bc - ac + bd

= ad - ac + bd + bc

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

= (a + b)(d - c) (= vế phải)

Vậy đpcm

Answer 2

BĐVT có,

=ab+ad-bc-cd-ab-ac+bd+cd

=ad-ac-bc+bd

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

=(a+b)(d-c)=vế phải

suy ra đpcm

tik nha

Answer 3

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

\(=ab+ad-cb-cd-ab-ac+bd+cd=ad-cb-ac+bd=\left(ad-ac\right)+\left(bd-bc\right)\)

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

Answer 4

Ta có: (a - c)(b + d) - (a - d)(b + c) = ab - bc + ad - cd - ab + bd - ac + cd

                                                  = ( ab - ab) + (cd - cd) + ad + bd - ac - bc

                                                  = ad + bd - ac - bc

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

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

      Tick cho mik nha bn