Действия над многочленами

Этот тренажёр поможет вам научиться работать с многочленами: складывать, вычитать, умножать их и раскладывать на множители. Вы будете выполнять задания, в которых нужно преобразовывать выражения, приводить подобные слагаемые и находить удобный способ разложения на множители.

Задания направлены на то, чтобы вы поняли, как устроены многочлены и как применять правила алгебры для упрощения выражений.

Тренажёр помогает:

• понять, что такое многочлен и его структура;
• научиться складывать и вычитать многочлены;
• освоить умножение многочленов;
• научиться раскладывать выражения на множители;
• развить навыки преобразования алгебраических выражений;
• подготовиться к самостоятельным и контрольным работам.

Рекомендуется внимательно выполнять каждое преобразование и проверять результат. Чтобы повторить тему, изучите уроки «Сложение и вычитание многочленов», «Умножение многочленов» и «Разложение многочленов на множители».

{"buttons":[],"questions":[{"text":"$(3x + 5) + (2x + 7)$","answer":0,"explanation":"$3x + 5 + 2x + 7 = 5x + 12$","correct_text":"$(3x + 5) + (2x + 7)=$ <<$5x + 12$>>","buttons":["$5x + 12$","$5x + 17$","$9x + 12$"]},{"text":"$(4a - 6) + (3a + 2)$","answer":2,"explanation":"$4a - 6 + 3a + 2 = 7a - 4$","correct_text":"$(4a - 6) + (3a + 2) =$ <<$7a - 4$>>","buttons":["$6a - 4$","$7a - 8$","$7a - 4$"]},{"text":"$(7x + 9) - (2x + 4)$","answer":1,"explanation":"$7x + 9 - 2x - 4 = 5x + 5$","correct_text":"$(7x + 9) - (2x + 4) =$ <<$5x + 5$>>","buttons":["$5x + 1$","$5x + 5$","$9x + 5$"]},{"text":"$(5y - 3) - (2y - 8)$","answer":0,"explanation":"$5y - 3 - 2y + 8 = 3y + 5$","correct_text":"$(5y - 3) - (2y - 8) =$ <<$3y + 5$>>","buttons":["$3y + 5$","$3y + 11$","$7y + 5$"]},{"text":"$(6a + 4b) + (3a + 5b)$","answer":1,"explanation":"$6a + 4b + 3a + 5b = 9a + 9b$","correct_text":"$(6a + 4b) + (3a + 5b) =$ <<$9a + 9b$>>","buttons":["$10a + 9b$","$9a + 9b$","$9a + 8b$"]},{"text":"$(8x - 2y) + (x + 7y)$","answer":0,"explanation":"$8x - 2y + x + 7y = 9x + 5y$","correct_text":"$(8x - 2y) + (x + 7y)=$ <<$9x + 5y$>>","buttons":["$15x + 3y$","$9x + 9y$","$9x + 5y$"]},{"text":"$(9m + 3n) - (4m + n)$","answer":2,"explanation":"$9m + 3n - 4m - n = 5m + 2n$","correct_text":"$(9m + 3n) - (4m + n) =$ <<$5m + 2n$>>","buttons":["$5m + 4n$","$13m + 2n$","$5m + 2n$"]},{"text":"$(10a - 5b) - (3a - 2b)$","answer":0,"explanation":"$10a - 5b - 3a + 2b = 7a - 3b$","correct_text":"$(10a - 5b) - (3a - 2b) =$ <<$7a - 3b$>>","buttons":["$7a - 3b$","$13a - 3b$","$7a - 7b$"]},{"text":"$(2x + 3y + 4) + (5x - y + 6)$","answer":1,"explanation":"$2x + 3y + 4 + 5x - y + 6 = 7x + 2y + 10$","correct_text":"$(2x + 3y + 4) + (5x - y + 6) =$ <<$7x + 2y + 10$>>","buttons":["$5x + 4y + 10$","$7x + 2y + 10$","$7x + 2y + 2$"]},{"text":"$(7a - 2b + 1) - (3a + b - 5)$","answer":0,"explanation":"$7a - 2b + 1 - 3a - b + 5 = 4a - 3b + 6$","correct_text":"$(7a - 2b + 1) - (3a + b - 5) =$ <<$4a - 3b + 6$>>","buttons":["$4a - 3b + 6$","$10a - 3b + 6$","$4a - b + 6$"]},{"text":"$(5x + 8) - (2x + 3)$","answer":0,"explanation":"$5x + 8 - 2x - 3 = 3x + 5$","correct_text":"$(5x + 8) - (2x + 3) =$ <<$3x + 5$>>","buttons":["$3x + 5$","$3x + 11$","$7x + 5$"]},{"text":"$(6a - 4) + (2a + 7)$","answer":1,"explanation":"$6a - 4 + 2a + 7 = 8a + 3$","correct_text":"$(6a - 4) + (2a + 7) =$ <<$8a + 3$>>","buttons":["$4a + 3$","$8a + 3$","$8a + 11$"]},{"text":"$(10y + 5) - (3y + 2)$","answer":2,"explanation":"$10y + 5 - 3y - 2 = 7y + 3$","correct_text":"$(10y + 5) - (3y + 2) =$ <<$7y + 3$>>","buttons":["$13y + 3$","$7y + 7$","$7y + 3$"]},{"text":"$(4b + 9) + (5b - 6)$","answer":0,"explanation":"$4b + 9 + 5b - 6 = 9b + 3$","correct_text":"$(4b + 9) + (5b - 6) =$ <<$9b + 3$>>","buttons":["$9b + 3$","$-b + 3$","$9b + 15$"]},{"text":"$(7x - 2) - (x + 5)$","answer":1,"explanation":"$7x - 2 - x - 5 = 6x - 7$","correct_text":"$(7x - 2) - (x + 5) =$ <<$6x - 7$>>","buttons":["$8x - 7$","$6x - 7$","$6x - 3$"]},{"text":"$(3a + 4b) + (2a - b)$","answer":1,"explanation":"$3a + 4b + 2a - b = 5a + 3b$","correct_text":"$(3a + 4b) + (2a - b) =$ <<$5a + 3b$>>","buttons":["$a + 3b$","$5a + 3b$","$5a + 5b$"]},{"text":"$(8m - 5n) - (3m + 2n)$","answer":0,"explanation":"$8m - 5n - 3m - 2n = 5m - 7n$","correct_text":"$(8m - 5n) - (3m + 2n) =$ <<$5m - 7n$>>","buttons":["$5m - 7n$","$5m - 3n$","$11m - 7n$"]},{"text":"$(2x + 7y + 1) + (3x - 2y + 4)$","answer":2,"explanation":"$2x + 7y + 1 + 3x - 2y + 4 = 5x + 5y + 5$","correct_text":"$(2x + 7y + 1) + (3x - 2y + 4) =$ <<$5x + 5y + 5$>>","buttons":["$5x + 9y + 5$","$-x + 5y + 5$","$5x + 5y + 5$"]},{"text":"$(9a - 3b + 2) - (4a + b - 1)$","answer":0,"explanation":"$9a - 3b + 2 - 4a - b + 1 = 5a - 4b + 3$","correct_text":"$(9a - 3b + 2) - (4a + b - 1) =$ <<$5a - 4b + 3$>>","buttons":["$5a - 4b + 3$","$5a - 2b + 3$","$5a - 4b + 1$"]},{"text":"$(6x + y - 8) + (2x + 3y + 5)$","answer":2,"explanation":"$6x + y - 8 + 2x + 3y + 5 = 8x + 4y - 3$","correct_text":"$(6x + y - 8) + (2x + 3y + 5) =$ <<$8x + 4y - 3$>>","buttons":["$4x + 4y - 3$","$8x + 4y - 13$","$8x + 4y - 3$"]},{"text":"$(2p + 3q) + (4p + 5q)$","answer":0,"explanation":"$2p + 3q + 4p + 5q = 6p + 8q$","correct_text":"$(2p + 3q) + (4p + 5q) =$ <<$6p + 8q$>>","buttons":["$6p + 8q$","$5p + 8q$","$6p + 9q$"]},{"text":"$(5v + 2w) + (3v + 6w)$","answer":2,"explanation":"$5v + 2w + 3v + 6w = 8v + 8w$","correct_text":"$(5v + 2w) + (3v + 6w) =$ <<$8v + 8w$>>","buttons":["$7v + 8w$","$8v + 9w$","$8v + 8w$"]},{"text":"$(7p + q) + (2p + 4q)$","answer":1,"explanation":"$7p + q + 2p + 4q = 9p + 5q$","correct_text":"$(7p + q) + (2p + 4q) =$ <<$9p + 5q$>>","buttons":["$8p + 5q$","$9p + 5q$","$9p + 6q$"]},{"text":"$(3z + 8v) - (z + 2v)$","answer":0,"explanation":"$3z + 8v - z - 2v = 2z + 6v$","correct_text":"$(3z + 8v) - (z + 2v) =$ <<$2z + 6v$>>","buttons":["$2z + 6v$","$11z + 6v$","$2z + 3v$"]},{"text":"$(6p + 5q) - (2p + 3q)$","answer":2,"explanation":"$6p + 5q - 2p - 3q = 4p + 2q$","correct_text":"$(6p + 5q) - (2p + 3q) =$ <<$4p + 2q$>>","buttons":["$11p + 2q$","$4p + 5q$","$4p + 2q$"]}],"no_uppercase":true}