Упростите выражения P + Q, P − Q и Q − P, если:
а) $P = 2x^2 + x - 2$, $Q = 1 + 2x - 2x^2$;
б) $P = 12 - 5a - 10a^2$, $Q = 10 + 4a - 10a^2$.
$P = 2x^2 + x - 2$, $Q = 1 + 2x - 2x^2$:
1) $P + Q = (2x^2 + x - 2) + (1 + 2x - 2x^2) = 2x^2 + x - 2 + 1 + 2x - 2x^2 = 3x - 1$;
2) $P - Q = (2x^2 + x - 2) - (1 + 2x - 2x^2) = 2x^2 + x - 2 - 1 - 2x + 2x^2 = 4x^2 - x - 3$;
3) $Q - P = (1 + 2x - 2x^2) - (2x^2 + x - 2) = 1 + 2x - 2x^2 - 2x^2 - x + 2 = -4x^2 + x + 3$.
$P = 12 - 5a - 10a^2$, $Q = 10 + 4a - 10a^2$:
1) $P + Q = (12 - 5a - 10a^2) + (10 + 4a - 10a^2) = 12 - 5a - 10a^2 + 10 + 4a - 10a^2 = -20a^2 - a + 22$;
2) $P - Q = (12 - 5a - 10a^2) - (10 + 4a - 10a^2) = 12 - 5a - 10a^2 - 10 - 4a + 10a^2 = -9a + 2$;
3) $Q - P = (10 + 4a - 10a^2) - (12 - 5a - 10a^2) = 10 + 4a - 10a^2 - 12 + 5a + 10a^2 = 9a - 2$.
Пожауйста, оцените решение