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Operaciones con monomios - Contenido educativo

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Subido el 10 de enero de 2024 por Juan De D.

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Se ve, ¿no? 00:00:00
Bueno, vamos a empezar con el óxido. 00:01:30
A ver, ¿se ve la pizarra? No escucho nada. ¿Se ve la pizarra? 00:01:45
No, se te ve a ti, Juan. Se te ve a ti. 00:02:11
Ah, no se ve la pizarra. 00:02:15
¿Ahora? 00:02:32
Sí, ahora sí se ve la pizarra. 00:02:36
Ah, vale. 00:02:40
Bueno, vamos con el álgebra. 00:02:49
Primero vamos a empezar a ver qué es una expresión algebraica, 00:02:54
que es toda expresión en la que aparecen números y letras relacionadas entre sí con operaciones armísticas, por ejemplo. 00:02:57
Pues esto es una expresión algebraica. Son números 2 por x más b. 00:03:10
Es una expresión algebraica. 00:03:23
Toda expresión en la que aparecen números y letras relacionados entre sí con operaciones armísticas. 00:03:25
O esta. 00:03:30
X más 3 por y. 00:03:36
Todo esto son expresiones aritméticas. 00:03:41
Es decir, es la mezcla de números con letras mediante operaciones aritméticas. 00:03:44
¿Y qué es el lenguaje algebraico? 00:04:11
Bueno, ¿qué es el lenguaje algebraico? 00:04:26
Pues es un sistema de expresión que emplea símbolos y números. 00:04:28
O sea, emplea expresiones algebraicas para expresar aquello que usan los números. 00:04:32
O sea, emplea expresiones algebraicas para expresar aquello que usualmente comunicamos mediante palabras 00:04:36
y que nos permite formular teoremas o resolver problemas y expresar propósitos. 00:04:42
Bueno, vamos a ver un ejemplo. 00:04:47
Aquí tenemos un ejemplo. 00:05:03
La suma de 5 más el triple del número a. 00:05:07
Pues 5 más 3 por a. 00:05:11
Ese sería un ejemplo. 00:05:13
La suma de 5 más el triple del número a. 00:05:16
5 más 3 por a. 00:05:19
¿Otro ejemplo? 00:05:21
Pues el área de un triángulo. 00:05:23
El área de un triángulo. 00:05:26
Si dibujáis un triángulo. 00:05:28
El área de un triángulo es 00:05:33
la base, que le llamamos b. 00:05:35
A la altura le llamamos h. 00:05:39
El área es b por h partido de 2. 00:05:41
Donde b es la base. 00:05:50
b es la base. 00:05:52
Y h es la altura. 00:05:54
Entonces utilizamos el lenguaje algebraico para expresar el área del triángulo. 00:05:57
Pues el área es la base, que le hemos llamado b. 00:06:28
Por la altura, partido de 2. 00:06:31
Esto es el lenguaje algebraico. 00:06:35
El área del triángulo. 00:06:37
Bueno, vamos a ver. 00:06:48
Vamos a empezar con la expresión algebraica más sencilla. 00:06:50
Soniendo las subtitulación. 00:06:58
Sonando las subtitulación. 00:07:03
Sonando las subtitulación. 00:07:07
Sonando las subtitulación. 00:07:09
Sonando las subtitulación. 00:07:14
Sonando las subtitulación. 00:07:18
Bueno, vamos a ver. 00:07:22
Esto del libro y esto nada. 00:07:24
No hay escaso o algo con el libro. 00:07:25
Vamos a ver. 00:07:27
Vamos a ver qué es un monomio. 00:07:33
Los monomios. 00:07:36
¿Qué es un monomio? 00:07:37
Pues es una expresión algebraica 00:07:39
formada por un número 00:07:42
y unas letras multiplicando. 00:07:46
Es decir, es un número 00:07:49
y letras que están multiplicándose. 00:07:51
Y las letras pueden tener exponentes. 00:07:54
Esto sería un monomio. 00:07:57
Tenemos un número que multiplica 00:07:59
a letras que se están multiplicando. 00:08:02
Y tiene un exponente. 00:08:04
Esto es un monomio. 00:08:07
Otro monomio, por ejemplo, es esto. 00:08:08
Otro monomio. 00:08:14
Esto está multiplicándose. 00:08:15
5 por x por y al cuadrado. 00:08:16
Nosotros vamos a utilizar 00:08:27
solo la letra x 00:08:32
para hacerlo más 00:08:35
más sencillo. 00:08:37
A ver si bien funciona esto. 00:08:44
Entonces. 00:08:57
Solo vamos a utilizar 00:09:19
la x 00:09:21
para multiplicar 00:09:23
Solo vamos a utilizar 00:09:24
la x con su exponente 00:09:26
para simplificar las cosas. 00:09:29
Entonces. 00:09:49
Vamos a utilizar un monomio 00:09:52
de este tipo. 00:09:53
Vamos a hacer monomios así. 00:09:54
Un número 00:09:56
una x 00:09:58
y un exponente. 00:09:59
Entonces. 00:10:04
El número va a ser 00:10:05
el coeficiente 00:10:06
y la letra con el exponente 00:10:12
vamos a llamar que es 00:10:15
la parte 00:10:17
literal. 00:10:19
La parte literal. 00:10:20
Y el exponente 00:10:24
y el exponente va a ser 00:10:27
el grado 00:10:29
del monomio. 00:10:32
O sea que en un monomio tenemos 00:10:43
el coeficiente 00:10:45
la parte literal 00:10:47
que es x a la cuarta 00:10:48
y el grado 00:10:50
que es el exponente que es 4. 00:10:51
Por ejemplo 00:11:12
en este monomio 00:11:13
menos 3x al cuadrado 00:11:15
¿Cuál es el coeficiente? 00:11:18
Menos 3. 00:11:23
El coeficiente es menos 3. 00:11:26
Es el número. 00:11:30
La parte literal 00:11:32
x elevado a 2. 00:11:36
La parte literal 00:11:38
es x elevado a 2. 00:11:40
x al cuadrado. 00:11:44
Y el grado 00:11:46
es el grado 2. 00:11:51
Coeficiente 00:11:55
parte literal 00:11:58
y grado 2. 00:12:00
También 00:12:05
podemos tener 00:12:06
coeficiente puede ser una fracción también. 00:12:15
3 medios de x al cuadrado. 00:12:22
Entonces ¿Cuál es el coeficiente? 00:12:25
Pues 3 medios ¿no? 00:12:31
La parte literal 00:12:33
x al cuadrado 00:12:38
y el grado 00:12:41
Y el grado 00:12:57
Bueno 00:13:09
ya sabemos lo que es un monomio 00:13:11
y las partes del monomio. 00:13:12
Ahora vamos a 00:13:15
a operar con monomios. 00:13:34
Vamos a ver 00:13:43
suma y resta de monomios. 00:13:44
Bueno. 00:14:13
¿Cómo se suma y resta monomios? 00:14:14
Voy a sacar los ejemplos que tengo aquí. 00:14:16
Bueno. 00:14:31
Suma y resta de monomios. 00:14:34
Solamente se pueden sumar o restar 00:14:36
los monomios que tengan la misma parte literal. 00:14:38
Es decir 00:14:40
solo se pueden sumar o restar 00:14:44
los monomios que tengan 00:14:46
la misma letra 00:14:48
o sea la x con el mismo exponente. 00:14:50
Vamos a ver un ejemplo. 00:14:54
3x al cuadrado 00:14:59
más 6 00:15:01
tienen que tener la misma parte literal 00:15:03
x cuadrado, x cuadrado. 00:15:05
La misma parte literal. 00:15:09
En este caso la misma x con la misma 00:15:12
la x con el mismo exponente. 00:15:14
Entonces ¿cómo se suma? 00:15:16
Se suman los coeficientes 00:15:21
se suman los coeficientes 00:15:24
es decir 3 más 6 00:15:27
y se queda la parte literal como está 00:15:31
9x al cuadrado. 00:15:33
Vamos a ver otro ejemplo. 00:15:36
Tenemos menos 4x al cubo 00:15:40
más 2x al cubo. 00:15:44
Primero hay que ver que tiene la misma parte literal 00:15:51
x cubo, x cubo. 00:15:53
Luego si se puede sumar. 00:15:58
¿Qué nos queda? 00:16:00
Menos 4 más 2 00:16:02
menos 2 00:16:05
x cubo. 00:16:07
Vamos a ver otro ejemplo. 00:16:12
7x menos 9x. 00:16:15
En este caso tenemos x 00:16:24
y x pues si se puede operar ¿no? 00:16:28
Operamos los coeficientes 00:16:32
7 menos 9 00:16:34
menos 2 00:16:37
menos 2x. 00:16:39
También pueden ser fracciones 00:16:56
5 cuartos 00:16:59
de x al cuadrado 00:17:01
menos 2 00:17:03
cuartos 00:17:04
de x al cuadrado. 00:17:06
Primero se pueden restar porque tenemos 00:17:08
x al cuadrado 00:17:10
y x al cuadrado. 00:17:12
Tenemos la misma 00:17:14
parte literal. 00:17:16
Se puede. 00:17:18
Pues entonces será 5 cuartos 00:17:20
menos 2 cuartos ¿no? 00:17:22
5 cuartos 00:17:24
menos 2 cuartos 00:17:25
es 3 cuartos. 00:17:27
Luego nos queda 00:17:30
3 cuartos 00:17:32
de x al cuadrado. 00:17:33
Se conserva la parte literal 00:17:37
y sumamos los coeficientes. 00:17:39
Y la suma de monomios 00:17:50
y resta no tiene más. 00:17:52
Voy a poner aquí unos ejercicios. 00:17:55
Ah bueno vamos a ver 00:17:57
por ejemplo esto. 00:17:59
¿Se puede hacer algo aquí? 00:18:04
No, no. 00:18:09
Se queda como está ¿no? 00:18:12
Aquí tenemos x al cuadrado 00:18:14
y aquí tenemos x. 00:18:17
Esto es igual a 00:18:20
menos 2x al cuadrado. 00:18:23
No se puede hacer nada. 00:18:24
Tiene que tener la misma parte literal. 00:18:28
Vamos a ver por ejemplo 00:18:29
menos 00:18:32
x al cuadrado 00:18:33
más 6x 00:18:34
aquí. 00:18:35
Aquí solo podemos sumar 00:18:37
lo que sea la misma parte literal. 00:18:38
Por ejemplo 00:18:41
las x con las x. 00:18:42
x con las x 00:18:45
pues 5 00:18:46
más 6 00:18:48
11x 00:18:50
más 6x 00:18:53
menos 00:18:54
x al cuadrado 00:18:56
y no se puede hacer más. 00:18:57
Aquí se acabó. 00:18:58
No se pueden sumar ni restar 00:19:03
si tienen distinta parte literal. 00:19:05
5x al cuadrado 00:19:22
menos 2x 00:19:23
más 00:19:26
al cuadrado. 00:19:28
Aquí ¿qué podríamos hacer? 00:19:30
Pues 00:19:33
x cuadrado 00:19:34
x cuadrado 00:19:35
pues aquí sí podemos sumar 00:19:37
5 más 3 00:19:38
x al cuadrado 00:19:42
5x al cuadrado 00:19:44
más 3x al cuadrado 00:19:46
y este aquí no podemos hacer nada. 00:19:48
Menos 2x 00:19:50
y ya no se puede hacer más. 00:19:53
Aquí se ha quedado. 00:19:54
Ahí se queda. 00:20:02
Venga, pues os pongo unos ejercicios para que hagáis. 00:20:13
Por ejemplo 00:20:23
100 00:22:11
101 00:22:12
102 00:22:13
103 00:22:14
104 00:22:15
105 00:22:16
106 00:22:17
100 00:23:42
100 00:23:43
100 00:23:44
100 00:23:45
100 00:23:46
100 00:23:47
100 00:23:48
100 00:23:49
100 00:23:50
100 00:23:51
100 00:23:52
100 00:23:53
100 00:23:54
100 00:23:55
100 00:23:56
100 00:23:57
100 00:23:58
100 00:23:59
100 00:24:00
100 00:24:01
100 00:24:02
100 00:24:03
100 00:24:04
100 00:24:05
100 00:24:06
100 00:24:07
100 00:24:08
100 00:24:09
100 00:24:10
100 00:24:11
100 00:24:12
100 00:24:13
100 00:24:14
100 00:24:15
100 00:24:16
100 00:24:17
100 00:24:18
100 00:24:19
100 00:24:20
100 00:24:21
100 00:24:22
100 00:24:23
100 00:24:24
100 00:24:29
100 00:24:30
100 00:24:31
100 00:24:32
100 00:24:33
100 00:24:34
100 00:24:35
100 00:24:36
100 00:24:37
100 00:24:38
100 00:24:39
100 00:24:40
100 00:24:42
100 00:24:43
100 00:24:44
100 00:24:45
100 00:24:46
100 00:24:47
100 00:24:48
100 00:24:49
100 00:24:50
100 00:24:51
100 00:24:52
100 00:24:54
100 00:24:55
100 00:24:56
100 00:24:57
100 00:24:58
110 00:24:59
110 00:25:00
110 00:25:01
110 00:25:02
111 00:25:03
110 00:25:04
111 00:25:05
110 00:25:06
110 00:25:08
110 00:25:09
110 00:25:10
110 00:25:11
110 00:25:12
110 00:25:13
110 00:25:14
115 00:25:15
115 00:25:16
115 00:25:17
115 00:25:18
115 00:25:19
115 00:25:20
115 00:25:21
115 00:25:22
115 00:25:23
115 00:25:24
115 00:25:25
151 00:25:26
151 00:25:27
152 00:25:28
152 00:25:29
153 00:25:30
153 00:25:31
154 00:25:32
155 00:25:33
155 00:25:34
156 00:25:35
157 00:25:36
158 00:25:37
159 00:25:38
151 00:25:39
152 00:25:40
153 00:25:41
154 00:25:42
155 00:25:43
156 00:25:44
157 00:25:45
158 00:25:46
159 00:25:47
1510 00:25:48
1511 00:25:49
1512 00:25:50
1513 00:25:51
1514 00:25:52
1515 00:25:53
1516 00:25:54
1517 00:25:55
1518 00:25:56
1519 00:25:57
1520 00:25:58
1521 00:25:59
1522 00:26:00
1523 00:26:01
1524 00:26:02
1525 00:26:03
1526 00:26:04
1527 00:26:05
1528 00:26:06
1529 00:26:07
1530 00:26:08
1531 00:26:09
1532 00:26:10
1533 00:26:11
1534 00:26:12
1535 00:26:13
1536 00:26:14
1537 00:26:15
1538 00:26:16
1539 00:26:17
1540 00:26:18
1541 00:26:19
1542 00:26:20
1543 00:26:21
1544 00:26:22
1545 00:26:23
1546 00:26:24
1547 00:26:25
1548 00:26:26
1549 00:26:27
1550 00:26:28
1551 00:26:29
1552 00:26:30
1553 00:26:31
1554 00:26:32
1555 00:26:33
1566 00:26:34
157 00:26:35
158 00:26:36
159 00:26:37
1510 00:26:38
1511 00:26:39
1512 00:26:40
1513 00:26:41
1514 00:26:42
1515 00:26:43
1516 00:26:44
1517 00:26:45
1518 00:26:46
1519 00:26:47
1520 00:26:48
1521 00:26:49
1522 00:26:50
1523 00:26:51
1524 00:26:52
1525 00:26:53
1526 00:26:54
1527 00:26:55
1528 00:26:56
1529 00:26:57
1530 00:26:58
1531 00:26:59
1532 00:27:00
1533 00:27:01
1534 00:27:02
1535 00:27:03
1537 00:27:04
1538 00:27:05
1539 00:27:06
1540 00:27:07
1541 00:27:08
1542 00:27:09
1543 00:27:10
1544 00:27:11
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1549 00:27:16
1550 00:27:17
1551 00:27:18
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1553 00:27:20
1554 00:27:21
1555 00:27:22
1556 00:27:23
1557 00:27:24
1558 00:27:25
1559 00:27:26
1560 00:27:27
1570 00:27:28
1571 00:27:29
1572 00:27:30
1573 00:27:31
1574 00:27:32
1575 00:27:33
1576 00:27:34
1577 00:27:35
1578 00:27:36
1579 00:27:37
1580 00:27:38
1581 00:27:39
1582 00:27:40
1583 00:27:41
1594 00:27:42
1595 00:27:43
1596 00:27:44
1507 00:27:45
1508 00:27:46
1509 00:27:47
1510 00:27:48
1511 00:27:49
1512 00:27:50
1513 00:27:51
1514 00:27:52
1515 00:27:53
1516 00:27:54
1517 00:27:55
1518 00:27:56
1519 00:27:57
1520 00:27:58
1521 00:27:59
1522 00:28:00
1523 00:28:01
1524 00:28:02
1525 00:28:03
1526 00:28:04
1527 00:28:05
1528 00:28:06
1529 00:28:07
1530 00:28:08
1531 00:28:09
1532 00:28:10
1533 00:28:11
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1535 00:28:13
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1538 00:28:16
1539 00:28:17
1540 00:28:18
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1544 00:28:22
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1548 00:28:26
1549 00:28:27
1550 00:28:28
1552 00:28:29
1553 00:28:30
1554 00:28:31
1555 00:28:32
1556 00:28:33
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1558 00:28:35
1559 00:28:36
1560 00:28:37
1570 00:28:38
1571 00:28:39
1572 00:28:40
1573 00:28:41
1574 00:28:42
1575 00:28:43
1576 00:28:44
1578 00:28:45
1579 00:28:46
1580 00:28:47
1581 00:28:48
1582 00:28:49
1583 00:28:50
1584 00:28:51
1595 00:28:52
1596 00:28:53
1597 00:28:54
1509 00:28:55
1510 00:28:56
1510 00:28:57
1511 00:28:59
1512 00:29:00
1513 00:29:01
1514 00:29:02
1515 00:29:03
1516 00:29:04
1517 00:29:05
1518 00:29:06
1519 00:29:07
1520 00:29:08
1521 00:29:09
1522 00:29:10
1523 00:29:11
1524 00:29:12
1525 00:29:13
1526 00:29:14
1527 00:29:15
1528 00:29:16
1529 00:29:17
1530 00:29:18
1531 00:29:19
1532 00:29:20
1533 00:29:21
1534 00:29:22
1535 00:29:23
1536 00:29:24
1537 00:29:25
1538 00:29:26
1539 00:29:27
1540 00:29:28
1541 00:29:29
1542 00:29:30
1543 00:29:31
1544 00:29:32
1545 00:29:33
1546 00:29:34
1547 00:29:35
1548 00:29:36
1549 00:29:37
1550 00:29:38
1551 00:29:39
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1553 00:29:41
1554 00:29:42
1555 00:29:43
1556 00:29:44
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1560 00:29:48
1570 00:29:49
1571 00:29:50
1572 00:29:51
1573 00:29:52
1574 00:29:53
1575 00:29:54
1576 00:29:55
1587 00:29:56
1589 00:29:57
1590 00:29:58
1591 00:29:59
1592 00:30:00
1593 00:30:01
1594 00:30:02
1505 00:30:03
1506 00:30:04
1507 00:30:05
1508 00:30:06
1509 00:30:07
1510 00:30:08
1511 00:30:09
1512 00:30:10
1513 00:30:11
1514 00:30:12
1515 00:30:13
1516 00:30:14
1517 00:30:15
1518 00:30:16
1519 00:30:17
1520 00:30:18
1521 00:30:19
1522 00:30:20
1523 00:30:21
1524 00:30:22
1525 00:30:23
1526 00:30:24
1527 00:30:25
1528 00:30:26
1529 00:30:27
1530 00:30:28
1531 00:30:29
1532 00:30:30
1533 00:30:31
1534 00:30:32
1535 00:30:33
1536 00:30:34
1537 00:30:35
1538 00:30:36
1539 00:30:37
1540 00:30:38
1541 00:30:39
1542 00:30:40
1543 00:30:41
1544 00:30:42
1545 00:30:43
1546 00:30:44
1547 00:30:45
1548 00:30:46
1549 00:30:47
1550 00:30:48
1551 00:30:49
1552 00:30:50
1553 00:30:51
1554 00:30:52
1555 00:30:53
1556 00:30:54
1557 00:30:55
1558 00:30:56
1559 00:30:57
1560 00:30:58
1570 00:30:59
1571 00:31:00
1572 00:31:01
1573 00:31:02
1574 00:31:03
1575 00:31:04
1576 00:31:05
1578 00:31:06
1579 00:31:07
1580 00:31:08
1581 00:31:09
1582 00:31:10
1583 00:31:11
1584 00:31:12
1585 00:31:13
1586 00:31:14
1587 00:31:15
1598 00:31:16
1599 00:31:17
1510 00:31:18
1510 00:31:19
1511 00:31:20
1512 00:31:21
1513 00:31:22
1514 00:31:23
1515 00:31:24
1516 00:31:25
1517 00:31:26
1518 00:31:27
1519 00:31:28
1520 00:31:29
1521 00:31:30
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Idioma/s:
es
Autor/es:
Juan de Dompablo Fantova
Subido por:
Juan De D.
Licencia:
Reconocimiento - No comercial - Compartir igual
Visualizaciones:
37
Fecha:
10 de enero de 2024 - 13:38
Visibilidad:
Público
Centro:
CEPAPUB ORCASITAS
Duración:
56′ 54″
Relación de aspecto:
1.78:1
Resolución:
1280x720 píxeles
Tamaño:
648.52 MBytes

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