Expresiones algebraicas, factorización y radicación. (Suma, Resta y Valor numérico de Expresiones algebraicas, Multiplicación y División de Expresiones algebraicas,Productos Notables de Expresiones algebraicas,Factorización por Productos Notables).
Suma, Resta y Valor numérico de Expresiones algebraicas.
Multiplicación y División de Expresiones algebraicas.
Productos Notables de Expresiones algebraicas.
Factorización por Productos Notables.
Un grupo de variables representadas por letras junto con un conjunto de números combinados con operaciones de suma, resta, multiplicación, división, potencia o extracción de raíces es llamado una expresión algebraica. Las expresiones algebraicas nos permiten, por ejemplo, hallar áreas y volúmenes
Suma, Resta y Valor numérico de Expresiones algebraicas.
Multiplicación y División de Expresiones algebraicas.
Productos Notables de Expresiones algebraicas.
Factorización por Productos Notables.
Suma, Resta y Valor numérico de Expresiones algebraicas.
Multiplicación y División de Expresiones algebraicas.
Productos Notables de Expresiones algebraicas.
Factorización por Productos Notables.
Un grupo de variables representadas por letras junto con un conjunto de números combinados con operaciones de suma, resta, multiplicación, división, potencia o extracción de raíces es llamado una expresión algebraica. Las expresiones algebraicas nos permiten, por ejemplo, hallar áreas y volúmenes
Suma, Resta y Valor numérico de Expresiones algebraicas.
Multiplicación y División de Expresiones algebraicas.
Productos Notables de Expresiones algebraicas.
Factorización por Productos Notables.
-Suma, Resta y Valor Numérico de Expresiones Algebraicas
-Multiplicación y División de Expresiones Algebraicas
-Productos Notables de Expresiones Algebraicas
-Factorización por Productos Notables
-Suma, Resta y Valor Numérico de Expresiones Algebraicas
-Multiplicación y División de Expresiones Algebraicas
-Productos Notables de Expresiones Algebraicas
-Factorización por Productos Notables
Algebraic Expression and Expansion.pptxMisbahSadia1
Algebraic expressions are fundamental mathematical constructs that play a crucial role in representing and solving a wide range of mathematical and real-world problems. They are composed of variables, constants, and mathematical operations, such as addition, subtraction, multiplication, and division. Algebraic expressions are a bridge between the abstract world of mathematics and the practical world of problem-solving.
Key components of an algebraic expression:
Variables: These are symbols (usually letters) that represent unknown values or quantities. Common variables include "x," "y," and "z." Variables allow us to generalize mathematical relationships and solve problems with unknowns.
Constants: These are fixed numerical values that do not change within the expression. Examples include numbers like 2, 5, π (pi), or any other specific constant value.
Mathematical Operations: Algebraic expressions include operations like addition (+), subtraction (-), multiplication (*), division (/), and exponentiation (^ or **). These operations define how the variables and constants interact within the expression.
Coefficients: Coefficients are the numerical values that multiply variables. For example, in the expression 3x, 3 is the coefficient of the variable x.
Algebraic expressions can take various forms, from simple linear expressions like 2x + 3 to more complex ones like (x^2 - 4)(x + 1). They are used in a wide range of mathematical contexts, including equations, inequalities, and functions.
Expansion of Algebraic Expressions:
Expanding an algebraic expression involves simplifying it by removing parentheses and combining like terms. This process is essential for solving equations, simplifying complex expressions, and gaining a better understanding of the underlying mathematical relationships.
Here's how to expand algebraic expressions:
Distribute: When an expression contains parentheses, you distribute each term within the parentheses to every term outside the parentheses using the appropriate mathematical operation (usually multiplication or addition).
Example: To expand 2(x + 3), you distribute the 2 to both terms inside the parentheses: 2x + 6.
Combine Like Terms: After distributing and simplifying, you look for like terms (terms with the same variable(s) and exponent(s)) and combine them.
Example: In the expression 3x + 2x, you combine the like terms to get 5x.
Remove Parentheses: If there are nested parentheses, continue to distribute and simplify until no parentheses remain.
Expanding algebraic expressions is a crucial step in solving equations and simplifying complex expressions. It allows mathematicians and scientists to manipulate and analyze mathematical relationships efficiently, making it an essential tool in various fields, including physics, engineering, and computer science.
Read| The latest issue of The Challenger is here! We are thrilled to announce that our school paper has qualified for the NATIONAL SCHOOLS PRESS CONFERENCE (NSPC) 2024. Thank you for your unwavering support and trust. Dive into the stories that made us stand out!
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The French Revolution, which began in 1789, was a period of radical social and political upheaval in France. It marked the decline of absolute monarchies, the rise of secular and democratic republics, and the eventual rise of Napoleon Bonaparte. This revolutionary period is crucial in understanding the transition from feudalism to modernity in Europe.
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Palestine last event orientationfvgnh .pptxRaedMohamed3
An EFL lesson about the current events in Palestine. It is intended to be for intermediate students who wish to increase their listening skills through a short lesson in power point.
The Roman Empire A Historical Colossus.pdfkaushalkr1407
The Roman Empire, a vast and enduring power, stands as one of history's most remarkable civilizations, leaving an indelible imprint on the world. It emerged from the Roman Republic, transitioning into an imperial powerhouse under the leadership of Augustus Caesar in 27 BCE. This transformation marked the beginning of an era defined by unprecedented territorial expansion, architectural marvels, and profound cultural influence.
The empire's roots lie in the city of Rome, founded, according to legend, by Romulus in 753 BCE. Over centuries, Rome evolved from a small settlement to a formidable republic, characterized by a complex political system with elected officials and checks on power. However, internal strife, class conflicts, and military ambitions paved the way for the end of the Republic. Julius Caesar’s dictatorship and subsequent assassination in 44 BCE created a power vacuum, leading to a civil war. Octavian, later Augustus, emerged victorious, heralding the Roman Empire’s birth.
Under Augustus, the empire experienced the Pax Romana, a 200-year period of relative peace and stability. Augustus reformed the military, established efficient administrative systems, and initiated grand construction projects. The empire's borders expanded, encompassing territories from Britain to Egypt and from Spain to the Euphrates. Roman legions, renowned for their discipline and engineering prowess, secured and maintained these vast territories, building roads, fortifications, and cities that facilitated control and integration.
The Roman Empire’s society was hierarchical, with a rigid class system. At the top were the patricians, wealthy elites who held significant political power. Below them were the plebeians, free citizens with limited political influence, and the vast numbers of slaves who formed the backbone of the economy. The family unit was central, governed by the paterfamilias, the male head who held absolute authority.
Culturally, the Romans were eclectic, absorbing and adapting elements from the civilizations they encountered, particularly the Greeks. Roman art, literature, and philosophy reflected this synthesis, creating a rich cultural tapestry. Latin, the Roman language, became the lingua franca of the Western world, influencing numerous modern languages.
Roman architecture and engineering achievements were monumental. They perfected the arch, vault, and dome, constructing enduring structures like the Colosseum, Pantheon, and aqueducts. These engineering marvels not only showcased Roman ingenuity but also served practical purposes, from public entertainment to water supply.
Acetabularia Information For Class 9 .docxvaibhavrinwa19
Acetabularia acetabulum is a single-celled green alga that in its vegetative state is morphologically differentiated into a basal rhizoid and an axially elongated stalk, which bears whorls of branching hairs. The single diploid nucleus resides in the rhizoid.
Welcome to TechSoup New Member Orientation and Q&A (May 2024).pdfTechSoup
In this webinar you will learn how your organization can access TechSoup's wide variety of product discount and donation programs. From hardware to software, we'll give you a tour of the tools available to help your nonprofit with productivity, collaboration, financial management, donor tracking, security, and more.
Biological screening of herbal drugs: Introduction and Need for
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2. 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:
4. 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:
6. 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.
8. 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
10. 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
12. 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
14. 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.
15. 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)