Упр.6.119 ГДЗ Дорофеев Суворова 7 класс (Алгебра)

а) (7 — 2х — х2) — (x — 2)(х + 3);
б) (3m2 + 3n2) — (2m + n)(m + 2n);
в) u(u + v) — (v — 1)(а — 1).

а)

$$ (7-2x-x^2)-(x-2)(x+3) $$
$$ ( x-2)(x+3)=x^2+3x-2x-6=x^2+x-6 $$
$$ 7-2x-x^2-(x^2+x-6)=7-2x-x^2-x^2-x+6 $$
$$ =-2x^2-3x+13 $$

б)

$$ (3m^2+3n^2)-(2m+n)(m+2n) $$
$$ (2m+n)(m+2n)=2m^2+4mn+mn+2n^2=2m^2+5mn+2n^2 $$
$$ 3m^2+3n^2-(2m^2+5mn+2n^2)=m^2-5mn+n^2 $$

в)

$$ u(u+v)-(v-1)(u-1) $$
$$ u(u+v)=u^2+uv $$
$$ (v-1)(u-1)=uv-v-u+1 $$
$$ u^2+uv-(uv-v-u+1)=u^2+uv-uv+v+u-1 $$
$$ =u^2+u+v-1 $$

Ответ

а) $$-2x^2-3x+13$$
б) $$m^2-5mn+n^2$$
в) $$u^2+u+v-1$$