Algebra is the study of mathematical symbols and rules for calculating those symbols, which allows numbers to be represented by variables. An algebraic expression combines constants and variables using operations like addition, subtraction, multiplication and division. Expressions can be monomials with one term, binomials with two terms, or trinomials with three terms. To multiply algebraic expressions, the signs and coefficients are multiplied, and the variables are multiplied using exponent rules.
Algebra is used in many field in many different ways to solve equation problems, and in business algebra is also used or in our day to day life it is also used. ... Algebra is a way of keeping track of unknown values, which can be used in equations.
I have added to the original presentation in response to one of the comments.... the result of 'x' is correct on slide 7, take a look at the new version of this ppt to clear up any confusion about why...
Algebra is used in many field in many different ways to solve equation problems, and in business algebra is also used or in our day to day life it is also used. ... Algebra is a way of keeping track of unknown values, which can be used in equations.
I have added to the original presentation in response to one of the comments.... the result of 'x' is correct on slide 7, take a look at the new version of this ppt to clear up any confusion about why...
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.
Are you scared of that algebraic sums? Just view this presentation an you can learn about each and every algebraic identities. Just view this and Now take full marks in your tests..
All the best to all students of class IX...This PPT will makes your difficulties easy to do....You will understand the polynomial chapter easily by seeing this ....Thanks for watching this ..Please Share, Like and Subscribe the PPT
Operation “Blue Star” is the only event in the history of Independent India where the state went into war with its own people. Even after about 40 years it is not clear if it was culmination of states anger over people of the region, a political game of power or start of dictatorial chapter in the democratic setup.
The people of Punjab felt alienated from main stream due to denial of their just demands during a long democratic struggle since independence. As it happen all over the word, it led to militant struggle with great loss of lives of military, police and civilian personnel. Killing of Indira Gandhi and massacre of innocent Sikhs in Delhi and other India cities was also associated with this movement.
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!
2024.06.01 Introducing a competency framework for languag learning materials ...Sandy Millin
http://sandymillin.wordpress.com/iateflwebinar2024
Published classroom materials form the basis of syllabuses, drive teacher professional development, and have a potentially huge influence on learners, teachers and education systems. All teachers also create their own materials, whether a few sentences on a blackboard, a highly-structured fully-realised online course, or anything in between. Despite this, the knowledge and skills needed to create effective language learning materials are rarely part of teacher training, and are mostly learnt by trial and error.
Knowledge and skills frameworks, generally called competency frameworks, for ELT teachers, trainers and managers have existed for a few years now. However, until I created one for my MA dissertation, there wasn’t one drawing together what we need to know and do to be able to effectively produce language learning materials.
This webinar will introduce you to my framework, highlighting the key competencies I identified from my research. It will also show how anybody involved in language teaching (any language, not just English!), teacher training, managing schools or developing language learning materials can benefit from using the framework.
How to Split Bills in the Odoo 17 POS ModuleCeline George
Bills have a main role in point of sale procedure. It will help to track sales, handling payments and giving receipts to customers. Bill splitting also has an important role in POS. For example, If some friends come together for dinner and if they want to divide the bill then it is possible by POS bill splitting. This slide will show how to split bills in odoo 17 POS.
Ethnobotany and Ethnopharmacology:
Ethnobotany in herbal drug evaluation,
Impact of Ethnobotany in traditional medicine,
New development in herbals,
Bio-prospecting tools for drug discovery,
Role of Ethnopharmacology in drug evaluation,
Reverse Pharmacology.
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.
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.
This is a presentation by Dada Robert in a Your Skill Boost masterclass organised by the Excellence Foundation for South Sudan (EFSS) on Saturday, the 25th and Sunday, the 26th of May 2024.
He discussed the concept of quality improvement, emphasizing its applicability to various aspects of life, including personal, project, and program improvements. He defined quality as doing the right thing at the right time in the right way to achieve the best possible results and discussed the concept of the "gap" between what we know and what we do, and how this gap represents the areas we need to improve. He explained the scientific approach to quality improvement, which involves systematic performance analysis, testing and learning, and implementing change ideas. He also highlighted the importance of client focus and a team approach to quality improvement.
How to Create Map Views in the Odoo 17 ERPCeline George
The map views are useful for providing a geographical representation of data. They allow users to visualize and analyze the data in a more intuitive manner.
3. Continue…
The word algebra comes from the title of the Arabic
book Ilm al-jabrwa’lmukābala by the Persian mathematician
and astronomer al-Khwarizmi. Algebra is the study of
mathematical symbols and rules for calculating these
symbols. In arithmetic, only numbers and their arithmetical
operations (such as +, −, ×, ÷) occur. In algebra, numbers are
often represented by symbols called variables.
4. ALGEBRAIC EXPRESSIONS
An algebraic expression is a combination of
constants and variables combined together with the help of
the four fundamental signs.
Any real number is a constant.
1, 5, –32, 73 , 2 - , 8.432, 1000000 and so on.
Letters used for representing unknown real numbers
called variables. Variables are x, y, a, b and so on
5. Types of expressions
MONOMIAL
An expression
with one term is
called a
monomial,
Examples
4x, 3𝑥2
y, − 2𝑦2
BINOMIAL
An expression
with two term is
called a binomial
Examples
2x + 3, 5𝑦2 + 9y,
𝑎2 𝑏2 + 2b .
TRINOMIAL
An expression
with three term
is called a
trinomial
Examples
2𝑎2
b − 8ab + 𝑏2
,
𝑥2
− n2 + 3 .
6. Some operations on algebraic expression
ADDITION SUBTRACTION
MULTIPLICATION DIVISION
7. MULTIPLICATION OF ALGEBRIC
EXPRESSIONS
Before doing the product of algebraic expressions, we
should follow the steps given below.
Step 1
• Multiply the signs of the terms.The product of two like signs
are positive and the product of two unlike signs are negative.
step2
• Multiply the corresponding co-efficients of the terms.
step3
• Multiply the variable factors by using laws of exponents.
8. There are four ways of multiplication on
algebraic expressions.
They are:
Product of a Monomial with a Monomial
Product of a Polynomial with a Monomial
Product of a Binomial with a Binomial
Product of a Polynomial with a Polynomial
9. EXAMPLE: Product of 2𝑦2
𝑥2
, 3𝑦2
z and – 𝑧2
𝑥3
( 2𝑦2
𝑥2
) × (3𝑦2
𝑧) × (−𝑧2
𝑥3
)
=(+) × (+) × (−)(2 × 3 ×1)(𝑥2 × 𝑥3)(𝑦2 × 𝑦2)(z × 𝑧2 )
= −6𝑥5 𝑦4 𝑧3
This is how multiply a monomial by a monomial
10. Example :Multiply (3xy + 7) by ( −4y )
(−4y) × (3xy + 7) =(−4y) ×(3xy) +(−4y)×(7)
= (−) × (+)(4 × 3)(x )( y × y )+ (−4 × 7)(y)
= −12x𝑦2 − 28y
This is how multiply a polynomial by a monomial
11. Example : Multiply (2x + 5y) and (3x − 4y)
(2x + 5y) (3x − 4y) = (2x)× (3x − 4y) + (5y)× (3x − 4y)
= 2 × 3 𝑥 × 𝑥 − 2 × 4 𝑥 × 𝑦 + 5 × 3
𝑦 × 𝑥 − (5 × 4)(𝑦 × 𝑦)
= 6𝑥2 − 8xy +15xy − 20𝑦2
= 6𝑥2
+ 7xy − 20𝑦2
(simplify the like terms)
This is how multiply a monomial by a monomial
12. CONCLUTION
We use algebra quite frequently in our
everyday lives, and without even
realizing it We not only use algebra, we
actually need algebra, to solve most of
our problems that involves calculations.