Даны три многочлена:
$p_1(a) = 2a^3 + 3a^2 - a + 1$;
$p_2(a) = 4a^4 + 6a^3 - 2a^2 + 2a$;
$p_3(a) = 2a^5 + 3a^4 - a^3 + a^2$.
Найдите:
а) $p(a) = p_1(a) + p_2(a) + p_3(a)$;
б) $p(a) = p_1(a) - p_2(a) + p_3(a)$;
в) $p(a) = p_1(a) + p_2(a) - p_3(a)$;
г) $p(a) = p_1(a) - p_2(a) - p_3(a)$.
$p(a) = p_1(a) + p_2(a) + p_3(a) = 2a^3 + 3a^2 - a + 1 + 4a^4 + 6a^3 - 2a^2 + 2a + 2a^5 + 3a^4 - a^3 + a^2 = 2a^5 + 7a^4 + 7a^3 + 2a^2 + a + 1$
$p(a) = p_1(a) - p_2(a) + p_3(a) = 2a^3 + 3a^2 - a + 1 - (4a^4 + 6a^3 - 2a^2 + 2a) + 2a^5 + 3a^4 - a^3 + a^2 = 2a^3 + 3a^2 - a + 1 - 4a^4 - 6a^3 + 2a^2 - 2a + 2a^5 + 3a^4 - a^3 + a^2 = 2a^5 - a^4 - 5a^3 + 6a^2 - 3a + 1$
$p(a) = p_1(a) + p_2(a) - p_3(a) = 2a^3 + 3a^2 - a + 1 + 4a^4 + 6a^3 - 2a^2 + 2a - (2a^5 + 3a^4 - a^3 + a^2) = 2a^3 + 3a^2 - a + 1 + 4a^4 + 6a^3 - 2a^2 + 2a - 2a^5 - 3a^4 + a^3 - a^2 = -2a^5 + a^4 + 9a^3 + a + 1$
$p(a) = p_1(a) - p_2(a) - p_3(a) = 2a^3 + 3a^2 - a + 1 - (4a^4 + 6a^3 - 2a^2 + 2a) - (2a^5 + 3a^4 - a^3 + a^2) = 2a^3 + 3a^2 - a + 1 - 4a^4 - 6a^3 + 2a^2 - 2a - 2a^5 - 3a^4 + a^3 - a^2 = -2a^5 - 7a^4 - 3a^3 + 4a^2 - 3a + 1$
Пожауйста, оцените решение
