Question

Show that (b-c)(x-a) (y-a) + ( c-a)(x-b)(y-b) + (a-b) (x-c)(y-c) is
independent of both x and y.​

Answer 1

Answer:

Hi there mate!!!!

let me help you

see, your question is simple. in order to confirm, you have to solve this equation.

Follow the following steps:-

(b-c)(x-a)(y-a) + (c-a)(x-b)(y-b) + (a-b)(x-c)(y-c)

=[bxy-bxa-bay+ba^2 -cxy+cxa+cay-ca^2] + [cxy -cxb -cby+cb^2 -axy +axb +aby -ab^2] + [axy -axc -acy +ac^2 -bxy +bxc +bcy -bc^2]

=bxy-bxa-bay+ba^2 -cxy+cxa+cay-ca^2+ cxy -cxb -cby+cb^2 -axy +axb +aby -ab^2+ axy -axc -acy +ac^2 -bxy +bxc +bcy -bc^2

=bxy-bxy -bxa+bxa -bay+bay +ba^2 -ba^2 -cxy +cxy + cxa-cxa +cay-cay -ca^2+ca^2 -cxb+cxb -cby+cby +cb^2-cb^2-axy+axy

=0+0+0+0+0+0+0+0+0+0+0+0

=0

:. it is verified, that (b-c)(x-a) (y-a) + ( c-a)(x-b)(y-b) + (a-b) (x-c)(y-c) is

independent of both x and y.

Hope you liked the answer

if you liked the answer please add for brainliest