Question

Докажите тождество
(5z^2-6k)^2-(5z^2+3k)^2+90z^2k=27k^2

Answer 1

(5z^2-6k)^2-(5z^2+3k)^2+90z^2k=
=(5z^2-6k+5z^2+3k)(5z^2-6k-5z^2-3k)+90z^2k=
=(10z^2-3k)(-9k)+90z^2k=
=-90z^2k+27k^2+90z^2k=27k^2