Действия над одночленами

Этот тренажёр поможет вам научиться выполнять действия с одночленами: складывать, вычитать и умножать их. Вы будете работать с выражениями, в которых нужно привести подобные слагаемые и правильно выполнять умножение одночленов.

Задания направлены на то, чтобы вы поняли, какие одночлены можно складывать и вычитать, а также как изменяются коэффициенты и степени при умножении.

Тренажёр помогает:

• понять, что такое одночлен и его коэффициент;
• научиться приводить подобные одночлены;
• освоить правила сложения и вычитания одночленов;
• научиться умножать одночлены;
• развить навыки аккуратных вычислений;
• подготовиться к самостоятельным и контрольным работам.

Рекомендуется внимательно следить за степенями переменных и коэффициентами. Чтобы повторить тему, изучите урок «Сложение и вычитание одночленов» и «Произведение одночленов».

{"buttons":[],"questions":[{"text":"$3x + 5x$","answer":0,"explanation":"$(3 + 5)x = 8x$","correct_text":"$3x + 5x = 8x$","buttons":["$8x$","$15x$","$-2x$"]},{"text":"$7a - 2a$","answer":2,"explanation":"$(7 - 2)a = 5a$","correct_text":"$7a - 2a = 5a$","buttons":["$9a$","$7a$","$5a$"]},{"text":"$4x \\cdot 3x$","answer":0,"explanation":"$(4 \\cdot 3)x^{1+1} = 12x^2$","correct_text":"$4x \\cdot 3x = 12x^2$","buttons":["$12x^2$","$12x$","$7x^2$"]},{"text":"$6y^2 \\cdot 2y$","answer":1,"explanation":"$(6 \\cdot 2)y^{2+1} = 12y^3$","correct_text":"$6y^2 \\cdot 2y = 12y^3$","buttons":["$12y^2$","$12y^3$","$8y^3$"]},{"text":"$8a^2 - 3a^2$","answer":2,"explanation":"$(8 - 3)a^2 = 5a^2$","correct_text":"$8a^2 - 3a^2 = 5a^2$","buttons":["$5a$","$5$","$5a^2$"]},{"text":"$2x + 9x$","answer":0,"explanation":"$(2 + 9)x = 11x$","correct_text":"$2x + 9x = 11x$","buttons":["$11x$","$-7x$","$11x^2$"]},{"text":"$10a - 4a$","answer":2,"explanation":"$(10 - 4)a = 6a$","correct_text":"$10a - 4a = 6a$","buttons":["$6a^2$","$14a$","$6a$"]},{"text":"$5x \\cdot 2x$","answer":0,"explanation":"$(5 \\cdot 2)x^{1+1} = 10x^2$","correct_text":"$5x \\cdot 2x = 10x^2$","buttons":["$10x^2$","$10x$","$7x^2$"]},{"text":"$3y^2 \\cdot 4y$","answer":1,"explanation":"$(3 \\cdot 4)y^{2+1} = 12y^3$","correct_text":"$3y^2 \\cdot 4y = 12y^3$","buttons":["$12y^2$","$12y^3$","$12y$"]},{"text":"$9b^2 - 5b^2$","answer":2,"explanation":"$(9 - 5)b^2 = 4b^2$","correct_text":"$9b^2 - 5b^2 = 4b^2$","buttons":["$4$","$4b$","$4b^2$"]},{"text":"$6m + 7m$","answer":1,"explanation":"$(6 + 7)m = 13m$","correct_text":"$6m + 7m = 13m$","buttons":["$13m^2$","$13m$","$-1m$"]},{"text":"$8c \\cdot 3c$","answer":2,"explanation":"$(8 \\cdot 3)c^{1+1} = 24c^2$","correct_text":"$8c \\cdot 3c = 24c^2$","buttons":["$5c^2$","$24c$","$24c^2$"]},{"text":"$12x - 5x$","answer":0,"explanation":"$(12 - 5)x = 7x$","correct_text":"$12x - 5x = 7x$","buttons":["$7x$","$7x^2$","$17x$"]},{"text":"$7k^2 \\cdot 2k^3$","answer":0,"explanation":"$(7 \\cdot 2)k^{2+3} = 14k^5$","correct_text":"$7k^2 \\cdot 2k^3 = 14k^5$","buttons":["$14k^5$","$14k^{-1}$","$14k^3$"]},{"text":"$11p^3 - 6p^3$","answer":2,"explanation":"$(11 - 6)p^3 = 5p^3$","correct_text":"$11p^3 - 6p^3 = 5p^3$","buttons":["$5$","$5p$","$5p^3$"]},{"text":"$3ab \\cdot 4a^2b^3$","answer":0,"explanation":"$(3 \\cdot 4)a^{1+2}b^{1+3} = 12a^3b^4$","correct_text":"$3ab \\cdot 4a^2b^3 = 12a^3b^4$","buttons":["$12a^3b^4$","$12ab$","$12a^4b^3$"]},{"text":"$5xy^2 \\cdot 2x^3y$","answer":2,"explanation":"$(5 \\cdot 2)x^{1+3}y^{2+1} = 10x^4y^3$","correct_text":"$5xy^2 \\cdot 2x^3y = 10x^4y^3$","buttons":["$10xy$","$7x^4y^3$","$10x^4y^3$"]},{"text":"$7mn^3 \\cdot 3m^2n$","answer":1,"explanation":"$(7 \\cdot 3)m^{1+2}n^{3+1} = 21m^3n^4$","correct_text":"$7mn^3 \\cdot 3m^2n = 21m^3n^4$","buttons":["$21m^3n$","$21m^3n^4$","$21mn^4$"]},{"text":"$6a^2b \\cdot 5ab^2$","answer":0,"explanation":"$(6 \\cdot 5)a^{2+1}b^{1+2} = 30a^3b^3$","correct_text":"$6a^2b \\cdot 5ab^2 = 30a^3b^3$","buttons":["$30a^3b^3$","$30a^2b^2$","$30a^2b^3$"]},{"text":"$4x^2y^3 \\cdot 3xy$","answer":2,"explanation":"$(4 \\cdot 3)x^{2+1}y^{3+1} = 12x^3y^4$","correct_text":"$4x^2y^3 \\cdot 3xy = 12x^3y^4$","buttons":["$12x^2y^3$","$12xy$","$12x^3y^4$"]},{"text":"$2abc \\cdot 3a^2b^2c^3$","answer":0,"explanation":"$(2 \\cdot 3)a^{1+2}b^{1+2}c^{1+3} = 6a^3b^3c^4$","correct_text":"$2abc \\cdot 3a^2b^2c^3 = 6a^3b^3c^4$","buttons":["$6a^3b^3c^4$","$6abc$","$6a^2b^2c^3$"]},{"text":"$5a^2bc \\cdot 4ab^3c^2$","answer":1,"explanation":"$(5 \\cdot 4)a^{2+1}b^{1+3}c^{1+2} = 20a^3b^4c^3$","correct_text":"$5a^2bc \\cdot 4ab^3c^2 = 20a^3b^4c^3$","buttons":["$20a^2b^3c^2$","$20a^3b^4c^3$","$20abc$"]},{"text":"$3ab^2c^3 \\cdot 2a^3bc$","answer":2,"explanation":"$(3 \\cdot 2)a^{1+3}b^{2+1}c^{3+1} = 6a^4b^3c^4$","correct_text":"$3ab^2c^3 \\cdot 2a^3bc = 6a^4b^3c^4$","buttons":["$6a^3b^3c^3$","$6ab^3c^3$","$6a^4b^3c^4$"]},{"text":"$7a^2b^3c \\cdot 2abc^2$","answer":0,"explanation":"$(7 \\cdot 2)a^{2+1}b^{3+1}c^{1+2} = 14a^3b^4c^3$","correct_text":"$7a^2b^3c \\cdot 2abc^2 = 14a^3b^4c^3$","buttons":["$14a^3b^4c^3$","$14abc$","$14a^2b^4c^2$"]},{"text":"$6abc^2 \\cdot 5a^2b^2c^3$","answer":2,"explanation":"$(6 \\cdot 5)a^{1+2}b^{1+2}c^{2+3} = 30a^3b^3c^5$","correct_text":"$6abc^2 \\cdot 5a^2b^2c^3 = 30a^3b^3c^5$","buttons":["$30a^2b^2c^5$","$30a^3b^3c^3$","$30a^3b^3c^5$"]},{"text":"$9a^2b - 5a^2b$","answer":0,"explanation":"$(9 - 5)a^2b = 4a^2b$","correct_text":"$9a^2b - 5a^2b = 4a^2b$","buttons":["$4a^2b$","$4ab$","$a^2b$"]},{"text":"$6ab^2 - 2ab^2$","answer":2,"explanation":"$(6 - 2)ab^2 = 4ab^2$","correct_text":"$6ab^2 - 2ab^2 = 4ab^2$","buttons":["$4a^2b$","$4ab$","$4ab^2$"]},{"text":"$7ab - 3ab$","answer":2,"explanation":"$(7 - 3)ab = 4ab$","correct_text":"$7ab - 3ab = 4ab$","buttons":["$4$","$ab$","$4ab$"]},{"text":"$10a^3b^2 - 7a^3b^2$","answer":1,"explanation":"$(10 - 7)a^3b^2 = 3a^3b^2$","correct_text":"$10a^3b^2 - 7a^3b^2 = 3a^3b^2$","buttons":["$3$","$3a^3b^2$","$3ab$"]},{"text":"$8a^2b^3 - 6a^2b^3$","answer":2,"explanation":"$(8 - 6)a^2b^3 = 2a^2b^3$","correct_text":"$8a^2b^3 - 6a^2b^3 = 2a^2b^3$","buttons":["$2$","$a^2b^3$","$2a^2b^3$"]}],"no_uppercase":true}