# Chapter 3 – Algebra

The following Topics and Sub-Topics are covered in this chapter and are available on MSVgo:

Introduction

Algebra is a subset of mathematics that deals with number theory, geometry, and analysis. It is one of the oldest divisions in the history of mathematics. According to other definitions, algebra is the analysis and manipulation of mathematical symbols and laws. Algebra covers a wide range of topics, from solving fundamental problems to studying abstractions. Algebra equations are included in several chapters in mathematics that students study in school. Also, algebra contains several formulas and identities.

#### What is the Concept of Algebra?

Algebra aids in the solution of statistical problems and the calculation of uncertain variables such as bank interest, proportions, and percentages. The variables in algebra may be used to describe undefined quantities combined in a way that allows the equations to be rewritten.

We use algebraic formulas to calculate distances, container volumes, and sales prices as required in our daily lives. Algebra is extremely useful in expressing a mathematical equation and relationship using letters or other symbols to describe the entities. The equation’s uncertain quantities can be overcome using mathematics.

1. Algebraic Branches
Algebra is a mathematical term dependent on variables or undefined values. Equations are a crucial principle of algebra. To execute arithmetic operations, it follows a set of laws used to interpret data sets with two or more variables. It is used to analyze a variety of topics in our setting. You’ll almost certainly use algebra without even realizing it. Elementary algebra, abstract algebra, commutative algebra, linear algebra and advanced algebra are algebra’s sub-branches.
2. Abstract Algebra
Abstract algebra is one of the branches of algebra that finds truths about algebraic structures regardless of certain operations’ existence. In certain instances, these procedures have special assets. As a result, we can draw conclusions about the implications of those properties. Abstract algebra is a subset of mathematics.Lands, sets, modules, circles, lattices, vector spaces, and other algebraic constructs are studied in abstract algebra.
3. Linear Algebra
Linear algebra is a type of algebra that can be used in both applied and pure mathematics. It is concerned with linear mappings between vector spaces. It also entails the investigation of planes and tracks. It involves the investigation of linear collections of equations with transformation properties. It is nearly universally found in mathematics. It is concerned with linear equations and their representation in vector spaces and by matrices for linear functions.
4. Commutative Algebra
Commutative algebra is a subset of mathematics that deals with commutative rings and their ideals. Commutative algebra is needed for algebraic number theory and algebraic geometry. Polynomial rings and rings of algebraic integers are some examples. Differential topology, invariant theory, order theory, and general topology are only a few of mathematics fields that use commutative algebra in various forms.

#### Framing Algebraic Expressions

Substituting a number for each vector and then conducting the arithmetic operations are the steps in evaluating an algebraic expression. We need to know the meaning of variables to substitute them with their meanings and compare the term.

The framing of a formula expresses a specified expression in the form of an algebraic equation.

#### Linear Equation in One Variable

The linear equations in one variable are written as ax+b = 0, where a and b are two integers and x is a variable, and there is only one solution. 3x+4=9, for example, is a linear equation of just one dimension. As a result, there is just one solution to this equation, which is x = 5/3.

Linear equation in one variable is one with a limit of one variable of order one. The formula is ax + b = 0, with x as the variable. There is just one solution to this equation.

#### Evaluation of Algebraic Expressions

A variable is a letter that describes an undefined number, such as x, y, or z.

3 + y = 10

You must substitute a number for each variable and execute the arithmetic operations to determine an algebraic expression. Since 3 + 7 = 10, the variable y is equivalent to 7 in the illustration above.

#### Conclusion

This chapter discusses the basics of algebra. We learn a method to solve algebraic equations using algebra substitution and the terminology associated with algebra.

#### FAQs

1. What do the fundamentals of algebra entail?
The basic operations in mathematics such as addition, subtraction, multiplication, and differentiation containing both constants and variables are covered in Basics of Algebra.
2. In algebra, what does the letter N stand for?
The use of pictures or letters to depict numbers is central to algebra. N reflects a particular number in an equation, not just any number.
3. What does the substitution approach imply?
The substitution procedure is commonly used in mathematics to solve a series of equations. Solve the equation for one variable first, then add the variable’s meaning in the other equation.
4. Mention the various techniques for solving linear equations in two variables in a scheme of equations.The following are three techniques for solving a two-variable scheme of linear equations:
• Form of substitution
• Form of elimination
• Type of cross-multiplication
5. What is the aim of ratio analysis?
Ratio analysis compares line-item details from financial statements to uncover information about a company’s performance, liquidity, operating quality, and solvency.

MSVgo is your one-stop solution for learning algebra through simple, interactive, and explanatory visualizations. Just try it for yourself once, and we’re sure you’ll be hooked on this interactive mode of learning.

### High School Physics

• Alternating Current
• Atoms
• Communication Systems
• Current Electricity
• Dual nature of Radiation and Matter
• Electric Charges and Fields
• Electricity
• Electromagnetic Induction
• Electromagnetic Waves
• Electrons and Photons
• Electrostatic Potential and Capacitance
• Fluid Pressure
• Force and Acceleration
• Force And Laws Of Motion
• Gravitation
• Internal Energy
• Kinetic Theory
• Law of motion
• Light – Reflection And Refraction
• Magnetic Effects Of Electric Current
• Magnetism and Matter
• Management Of Natural Resources
• Mechanical properties of Fluids
• Mechanical properties of Solids
• Motion
• Motion in a plane
• Motion in a straight line
• Moving Charges and Magnetism
• Nuclear Energy
• Nuclei
• Oscillations
• Our Environment
• Paths of Heat
• Physical world
• Ray optics and optical instruments
• Semiconductor Devices
• Semiconductor Electronics: Materials, Devices and Simple Circuits
• Simple Machines
• Sound
• Sources Of Energy
• Specific and Latent Heats
• Spherical Mirrors
• Static Electricity
• Systems of Particles and Rotational motion
• Thermal properties of matter
• Thermodynamics
• Units and Measurement
• Vectors, Scalar Quantities and Elementary Calculus
• Wave Optics
• Waves
• Work, Power and Energy

### High School Chemistry

• Acids, Bases and Salts
• Alcohols, Phenols and Ethers
• Aldehydes, Ketones and Carboxylic Acids
• Aliphatic and Aromatic Hydrocarbons
• Alkyl and Aryl Halides
• Amines
• Analytical Chemistry
• Atomic Structure
• Atoms And Molecules
• Basic concepts of Chemistry
• Biomolecules
• Carbon And Its Compounds
• Carboxylic acids and Acid Derivatives
• Chemical Bonding and Molecular Structures
• Chemical Energetics
• Chemical Equilibria
• Chemical Kinetics
• Chemical Reactions And Equations
• Chemical Reactions and Their Mechanisms
• Chemistry in Everyday Life
• Chemistry of p-Block elements
• Chemistry of Transition and Inner Transition
• Classification of Elements
• Coordination Compounds
• Cyanide, Isocyanide, Nitro compounds and Amines
• Electrochemistry
• Electrolysis
• Elements, Compounds and Mixtures
• Environmental Chemistry
• Equilibrium
• Ethers and Carbonyl compounds
• Haloalkanes and Haloarenes
• Hydrocarbons
• Hydrogen
• Ideal solutions
• Introduction to Organic Chemistry
• Ionic equilibria
• Matter
• Matter Around Us
• Matter In Our Surroundings
• Metallurgy
• Metals And Non-Metals
• Mole Concept and Stoichiometry
• Natural Resources
• Organic Chemistry – Basic Principles
• Periodic Classification of Elements
• Physical and Chemical Changes
• Physical and Chemical Properties of Water
• Polymers
• Preparation, Properties and Uses of Compounds
• Principles and Processes of Isolation of Elements
• Redox Reactions
• Relative Molecular Mass and Mole
• States of Matter
• Structure Of The Atom
• Study of Compounds
• Study of Gas Laws
• Study of Representative Elements
• Surface Chemistry
• The d-block and f-block elements
• The Gaseous State
• The p-Block Elements
• The Periodic Table
• The s-Block Elements
• The Solid State
• Thermodynamics

### High School Biology

• Absorption and Movement of Water in Plants
• Anatomy of Flowering Plants
• Animal Kingdom
• Bacteria and Fungi-Friends and Foe
• Biodiversity and Conservation
• Biofertilizers
• Biological Classification
• Biomedical Engineering
• Biomolecules
• Biotechnology and its Applications
• Biotic Community
• Body Fluids and Circulation
• Breathing and Exchange of Gases
• Cell – Unit of Life
• Cell Cycle and Cell Division
• Cell Division and Structure of Chromosomes
• Cell Reproduction
• Cellular Respiration
• Chemical Coordination and Integration
• Circulation
• Control And Coordination
• Crop Improvement
• Digestion and Absorption
• Diversity In Living Organisms
• Ecosystem
• Environmental Issues
• Excretory Products and their Elimination
• Flowering Plants
• Genes and Chromosomes
• Health and Diseases
• Health and Its Significance
• Heredity And Evolution
• Heredity and Variation
• How Do Organisms Reproduce?
• Human Diseases
• Human Eye And Colourful World
• Human Health and Disease
• Human Population
• Human Reproduction
• Hygiene
• Improvement In Food Resources
• Integumentary System- Skin
• Kingdom Fungi
• Kingdom Monera
• Kingdom Protista
• Life Processes
• Locomotion and Movement
• Microbes in Human Welfare
• Mineral Nutrition
• Molecular Basis of Inheritance
• Morphology of Flowering Plants
• Neural Control And Coordination
• Nutrition in Human Beings
• Organism and Population
• Photosynthesis
• Photosynthesis in Higher Plants
• Plant Growth and Development
• Plant Kingdom
• Pollination and Fertilization
• Pollution; Sources and its effects
• Principles of Inheritance and Variation
• Reproduction and Development in Angiosperms
• Reproduction in Organisms
• Reproductive Health
• Respiration in Human Beings
• Respiration in Plants
• Respiratory System
• Sexual Reproduction in Flowering Plants
• Strategies for Enhancement in Food Production
• Structural Organisation in Animals
• Structural Organisation of the Cell
• The Endocrine System
• The Fundamental Unit Of Life
• The Living World
• The Nervous System and Sense Organs
• Tissues
• Transpiration
• Transport in Plants

### High School Math

• Algebra – Arithmatic Progressions
• Algebra – Complex Numbers and Quadratic Equations
• Algebra – Linear Inequalities
• Algebra – Pair of Linear Equations in Two Variables
• Algebra – Polynomials
• Algebra – Principle of Mathematical Induction
• Binomial Theorem
• Calculus – Applications of Derivatives
• Calculus – Applications of the Integrals
• Calculus – Continuity and Differentiability
• Calculus – Differential Equations
• Calculus – Integrals
• Geometry – Area
• Geometry – Circles
• Geometry – Conic Sections
• Geometry – Constructions
• Geometry – Introduction to Euclid’s Geometry
• Geometry – Three-dimensional Geometry
• Geometry – Lines and Angles
• Geometry – Straight Lines
• Geometry – Triangles
• Linear Programming
• Matrices and Determinants
• Mensuration – Areas
• Mensuration – Surface Areas and Volumes
• Number Systems
• Number Systems – Real Numbers
• Permutations and Combinations
• Probability
• Sequence and Series
• Sets and Functions
• Statistics
• Trignometry – Height and Distance
• Trignometry – Identities
• Trignometry – Introduction

### Middle School Science

• Acids, Bases And Salts
• Air and Its Constituents
• Basic Biology
• Body Movements
• Carbon and Its Compounds
• Cell – Structure And Functions
• Changes Around Us
• Chemical Effects Of Electric Current
• Coal And Petroleum
• Combustion And Flame
• Components Of Food
• Conservation Of Plants And Animals
• Crop Production And Management
• Electric Current And Its Effects
• Electricity And Circuits
• Elements and Compounds
• Fibre To Fabric
• Food production and management
• Force And Pressure
• Forests: Our Lifeline
• Friction
• Fun With Magnets
• Garbage In, Garbage Out
• Getting To Know Plants
• Health and Hygiene
• Heat
• Hydrogen
• Life Processes: Nutrition in Animals and Plants
• Materials: Metals And Non-Metals
• Matter and Its States
• Metals and Non-metals
• Micro Organisms: Friend And Foe
• Motion And Measurement Of Distances
• Motion And Time
• Nutrition In Animals
• Nutrition In Plants
• Organization in Living Things
• Our Environment
• Physical And Chemical Changes
• Pollution and conservation
• Pollution Of Air And Water
• Reaching The Age Of Adolescence
• Reproduction In Animals
• Reproduction In Plants
• Respiration In Organisms
• Rocks and Minerals
• Separation Of Substances
• Simple Machines
• Soil
• Some Natural Phenomena
• Sorting Materials Into Groups
• Sound
• Stars And The Solar System
• Structure of Atom
• Synthetic Fibers And Plastics
• The Living Organisms And Their Surroundings
• Transfer of Heat
• Transformation of Substances
• Transportation In Animals And Plants
• Universe
• Waste-water Story
• Water: A Precious Resource
• Weather, Climate And Adaptations Of Animals To Climate
• Winds, Storms And Cyclones

### Middle School Math

• Area and Its Boundary
• Boxes and Sketches
• Data Handling
• Fun With Numbers
• Heavy and Light
• How Many
• Long And Short
• Mapping
• Measurement
• Money
• Multiplication and Factors
• Multiply and Divide
• Numbers
• Parts and Wholes
• Pattern Recognition
• Patterns
• Play With Patterns
• Rupees And Paise
• Shapes And Angles
• Shapes And Designs
• Shapes and Space
• Similarity
• Smart Charts
• Squares
• Subtraction
• Tables And Shares
• Tenths and Hundredths
• Time