Вправи: 359

359. Спрости вираз:

a) 1(a-b)(b- c) + 1(c- a)(a- b) + 1(b- c)(c- a) = c-a + b- c (a- b)(b- c)(c- a) + 1(b- c)(c- a) = b- a(a- b)(b- c)(c-a) + 1(b- c)(c- a) = -1(b- c)(c-a) + 1(b-c)(c- a) = 0;

б) x2(x- y)(x- z) + y2(y - x)(y- z) + z2(z- x)(z- y) = x2y-x2z- xy2+y2z (x- y)(x- z)(y- z) + z2(z- x)(z- y) = x2y- x2z- xy2+y2z(x- y)(x- z)(y- z) + z2(z- x)(z- y) = x2y-x2z- xy2+y2z+ xz2- yz2 (x- y)(x- z)(y- z) = xyx- y- z(x2-y2)+ z2(x- y) (x- y)(x- z)(y-z) = (x- y)(xy- zx- zy+ z2)x- yx- z(y- z) = xy- z- z(y- z)x- z(y- z) = (y- z)(x- z)(x- z)(y-z) = 1.