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Expresiones
Algebraicas
Estudiante:
Rubí Prieto
Nro. Cedula:
30.395.948
Sección:
0101.
Materia:
Matemática.
República Bolivariana de Venezuela
Ministerio del poder popular para la educación
Universidad Politécnica Territorial Andrés Eloy Blanco
Si dos monomios son semejantes, sumamos o
restamos los coeficientes y dejamos el mismo literal.
Si no son semejantes, esta operación no puede
expresarse de manera más simplificada. 3x+2x=5x,
pero las expresiones 3x2+2x o 2x+7y no se pueden
simplificar.
Ejemplo:
Suma, resta de expresiones algebraicas.
Monomios:
Ejercicios:
1)
2)
Resta
Dos o más monomios solo se pueden restar si
son monomios semejantes, es decir, si ambos
monomios tienen una parte literal idéntica
(mismas letras y mismos exponentes).
La resta de dos monomios semejantes es igual a
otro monomio compuesto por la misma parte
literal y la resta de los coeficientes de esos dos
monomios.
Monomios:
Ejercicios:
1)
Dados los monomios: y
Encontrar calculamos el opuesto al
segundo polinomio.
2)
Valor numérico de expresiones algebraicas
Valor numérico Si en una expresión algebraica sustituimos las
letras (variables) por números, lo que tendremos será una
expresión numérica. El resultado de esta expresión es lo que
llamamos valor numérico de la expresión algebraica para esos
valores de las variable.
Calcular el valor numérico para:
𝑥 + 15
cuando 𝑥 = 2.
Sustituimos en la expresión:
𝑥 + 15 = 2 + 15 = 17
El valor numérico de la expresión es 17.
Ejercicios:
1)
2)
Multiplicación y división de expresiones
algebraicas
Multiplicación de dos monomios. Para esta operación se debe de
aplicar la regla de los signos, los coeficientes se multiplican y las
literales cuando son iguales se escribe la literal y se suman los
exponentes, si las literales son diferentes se pone cada literal con su
correspondiente exponente.
Monomios
Ejemplo:
Multiplicar 3x3y2 por 7x4
=(3x3y2)(7x4)
Se realiza de la siguiente forma: los coeficientes se multiplican, el
exponente de x es la suma de los exponentes que tiene en cada
factor y como y solo esta en uno de los factores se escribe y con su
propio exponente.
(3)(7)x3+4y2
21x7y2
Ejercicios:
(3x2 . 5x) + (3x2 . -4x3) + (3x2 + 3) =
(3.5)x2+1 + (3.-4)x2+3 + (3.3)x2 =
(15)x3 + (-12)x5 +(9)x2 =
15x3 – 12x5 + 9x2
= 15x3 – 12x5 + 9x2
1)
(5x³y) × (- 3y4z)
(5x³y) × (- 3y4z) = – 15x3y5z
2)
División de dos monomios. En esta operación se vuelve aplicar la
regla de los signos, en cuanto a los demás elementos se aplican las
siguientes reglas: se dividen los coeficientes, si esto es posible, en
cuanto a las literales si hay alguna que este tanto en el numerador
como en el denominador, si el exponente del numerador es el
mayor se pone la literal en el numerador y al exponente se le resta
el exponente de la literal del denominador, en caso contrario se
pone la literal en el denominador y a su exponente se le resta el del
numerador.
División
Dividir 9x3y2 entre 3x2w
=9x3y2 / 3x2w
=9x3y2 / 3x2w = 3xy2 / w
Ejercicios:
1)
2)
y
Producto notable de expresiones algebraicas
productos notables son expresiones algebraicas que se encuentran
frecuentemente y que es preciso saber factorizarlas a simple vista; es decir,
sin necesidad de hacerlo paso por paso.
•Se les llama productos notables .precisamente porque son muy utilizados
en los ejercicios. A continuación veremos algunas expresiones algebraicas y
del lado derecho de la igualdad se muestra la forma de factorizarlas (mostrada
como un producto notable). Cuadrado de la suma de dos cantidades o
binomio cuadrado
a2 + 2ab + b2 = (a + b)2
El cuadrado de la suma de dos cantidades es igual al cuadrado de la primera
cantidad, más el doble de la primera cantidad multiplicada por la segunda,
más el cuadrado de la segunda cantidad. Ejemplo:
Entonces, para entender de lo que hablamos, cuando nos
encontramos con una expresión de la forma a2 + 2ab + b2 debemos
identificarla de inmediato y saber que
podemos factorizarla como (a + b)2
Ejercicios:
1)
2)
Factorización de expresiones algebraicas
• Identificar si la expresión algebraica
posee términos en común.
• Obtener el máximo común divisor
(M.C.D.) de los coeficientes numéricos.
Ejercicios:
n x 2 + 2xy + y 2 − 3x − 3y − 4
x 2 + 2xy + y 2 − 3x − 3y − 4 = (x + y) 2 −
3(x + y) − 4
= ((x + y) + 1)((x + y) − 4)
= (x + y + 1)(x + y − 4)
1)
2)
Bibliografía:
•http://descartes.cnice.mec.es/materiales_didacticos/EDAD_2eso_expre
siones_algebraicas/2quincena5_contenidos_2b.htm
•https://proyectodescartes.org/EDAD/materiales_didacticos/EDAD_2eso
_expresiones_algebraicas-JS-LOMCE/2esoquincena5.pdf
•http://cidecame.uaeh.edu.mx/lcc/mapa/PROYECTO/libro1/153_multipli
cacin_de_expresiones_algebraicas.html#:~:text=Multiplicaci%C3%B3n%2
0de%20dos%20monomios.,literal%20con%20su%20correspondiente%2
0exponente.
•http://recursostic.educacion.es/descartes/web/materiales_didacticos/
EDAD_2eso_expresiones_algebraicas/2esoquincena5.pdf
•https://sites.google.com/site/algebrageneralidadesii/productos-
notables-o-
especiales#:~:text=Se%20llama%20productos%20notables%20a,muy%2
0utilizados%20en%20los%20ejercicios.
•http://ftp.campusvirtual.utn.ac.cr/calculo/Factorizacion.pdf

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Algebraic Expressions Guide