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МатематикаВопрос:
Задание 50. Найдите сумму и разность многочленов: a b a+b a-b 1) x+y x-y (x + y) + (x - y) = x+y+x-y=2x (x+y)(xy)=x+y-x + y = 2y 2) m-n m + 12 M+n+M+n= 3) -k-c k-c 4) 3s-2q 2q-3s 5) 5c + d d-5c 6) 3x-r -3x-r 7) 2y + t 3y-t 8) x² + y² x² + t² 9) xy+2 -xy + 2 10) xy² + x²y 3xy² - x²y 11) -x-3y -x-5y 12) 8npq+7-7-8npq
Ответ:
Привет! Давай выполним это задание по алгебре. Нам нужно найти сумму и разность многочленов для каждого случая. Сейчас мы это сделаем!
1) a = x + y, b = x - y * a + b = (x + y) + (x - y) = x + y + x - y = 2x * a - b = (x + y) - (x - y) = x + y - x + y = 2y 2) a = m - n, b = m + n * a + b = (m - n) + (m + n) = m - n + m + n = 2m * a - b = (m - n) - (m + n) = m - n - m - n = -2n 3) a = -k - c, b = k - c * a + b = (-k - c) + (k - c) = -k - c + k - c = -2c * a - b = (-k - c) - (k - c) = -k - c - k + c = -2k 4) a = 3s - 2q, b = 2q - 3s * a + b = (3s - 2q) + (2q - 3s) = 3s - 2q + 2q - 3s = 0 * a - b = (3s - 2q) - (2q - 3s) = 3s - 2q - 2q + 3s = 6s - 4q 5) a = 5c + d, b = d - 5c * a + b = (5c + d) + (d - 5c) = 5c + d + d - 5c = 2d * a - b = (5c + d) - (d - 5c) = 5c + d - d + 5c = 10c 6) a = 3x - r, b = -3x - r * a + b = (3x - r) + (-3x - r) = 3x - r - 3x - r = -2r * a - b = (3x - r) - (-3x - r) = 3x - r + 3x + r = 6x 7) a = 2y + t, b = 3y - t * a + b = (2y + t) + (3y - t) = 2y + t + 3y - t = 5y * a - b = (2y + t) - (3y - t) = 2y + t - 3y + t = -y + 2t 8) a = x² + y², b = x² + t² * a + b = (x² + y²) + (x² + t²) = x² + y² + x² + t² = 2x² + y² + t² * a - b = (x² + y²) - (x² + t²) = x² + y² - x² - t² = y² - t² 9) a = xy + 2, b = -xy + 2 * a + b = (xy + 2) + (-xy + 2) = xy + 2 - xy + 2 = 4 * a - b = (xy + 2) - (-xy + 2) = xy + 2 + xy - 2 = 2xy 10) a = xy² + x²y, b = 3xy² - x²y * a + b = (xy² + x²y) + (3xy² - x²y) = xy² + x²y + 3xy² - x²y = 4xy² * a - b = (xy² + x²y) - (3xy² - x²y) = xy² + x²y - 3xy² + x²y = -2xy² + 2x²y 11) a = -x - 3y, b = -x - 5y * a + b = (-x - 3y) + (-x - 5y) = -x - 3y - x - 5y = -2x - 8y * a - b = (-x - 3y) - (-x - 5y) = -x - 3y + x + 5y = 2y 12) a = 8npq + 7, b = -7 - 8npq * a + b = (8npq + 7) + (-7 - 8npq) = 8npq + 7 - 7 - 8npq = 0 * a - b = (8npq + 7) - (-7 - 8npq) = 8npq + 7 + 7 + 8npq = 16npq + 14
1) a = x + y, b = x - y * a + b = (x + y) + (x - y) = x + y + x - y = 2x * a - b = (x + y) - (x - y) = x + y - x + y = 2y 2) a = m - n, b = m + n * a + b = (m - n) + (m + n) = m - n + m + n = 2m * a - b = (m - n) - (m + n) = m - n - m - n = -2n 3) a = -k - c, b = k - c * a + b = (-k - c) + (k - c) = -k - c + k - c = -2c * a - b = (-k - c) - (k - c) = -k - c - k + c = -2k 4) a = 3s - 2q, b = 2q - 3s * a + b = (3s - 2q) + (2q - 3s) = 3s - 2q + 2q - 3s = 0 * a - b = (3s - 2q) - (2q - 3s) = 3s - 2q - 2q + 3s = 6s - 4q 5) a = 5c + d, b = d - 5c * a + b = (5c + d) + (d - 5c) = 5c + d + d - 5c = 2d * a - b = (5c + d) - (d - 5c) = 5c + d - d + 5c = 10c 6) a = 3x - r, b = -3x - r * a + b = (3x - r) + (-3x - r) = 3x - r - 3x - r = -2r * a - b = (3x - r) - (-3x - r) = 3x - r + 3x + r = 6x 7) a = 2y + t, b = 3y - t * a + b = (2y + t) + (3y - t) = 2y + t + 3y - t = 5y * a - b = (2y + t) - (3y - t) = 2y + t - 3y + t = -y + 2t 8) a = x² + y², b = x² + t² * a + b = (x² + y²) + (x² + t²) = x² + y² + x² + t² = 2x² + y² + t² * a - b = (x² + y²) - (x² + t²) = x² + y² - x² - t² = y² - t² 9) a = xy + 2, b = -xy + 2 * a + b = (xy + 2) + (-xy + 2) = xy + 2 - xy + 2 = 4 * a - b = (xy + 2) - (-xy + 2) = xy + 2 + xy - 2 = 2xy 10) a = xy² + x²y, b = 3xy² - x²y * a + b = (xy² + x²y) + (3xy² - x²y) = xy² + x²y + 3xy² - x²y = 4xy² * a - b = (xy² + x²y) - (3xy² - x²y) = xy² + x²y - 3xy² + x²y = -2xy² + 2x²y 11) a = -x - 3y, b = -x - 5y * a + b = (-x - 3y) + (-x - 5y) = -x - 3y - x - 5y = -2x - 8y * a - b = (-x - 3y) - (-x - 5y) = -x - 3y + x + 5y = 2y 12) a = 8npq + 7, b = -7 - 8npq * a + b = (8npq + 7) + (-7 - 8npq) = 8npq + 7 - 7 - 8npq = 0 * a - b = (8npq + 7) - (-7 - 8npq) = 8npq + 7 + 7 + 8npq = 16npq + 14
Ответ: Выше приведены суммы и разности для каждого случая.
Отлично! Теперь ты знаешь, как складывать и вычитать многочлены. Продолжай в том же духе, и у тебя всё получится!