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Algebra Terminologies
The document introduces some key terms used in algebra. It defines an algebraic term as having a numerical coefficient and one or more literal coefficients. Like terms are terms that have the same literal coefficient, while unlike terms have different literal coefficients. Algebraic expressions are formed by combining algebraic terms with addition or subtraction. Expressions can be monomial, binomial, trinomial or polynomial depending on the number of terms. Finally, an equation is defined as a statement that sets the left-hand side equal to the right-hand side.
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Overview of algebra as the mathematics of unknowns using letters and basic operations like addition and subtraction.
Definition of algebraic terms including numerical and literal coefficients, with examples of valid terms.
Classification of algebraic terms into like terms (same literal coefficients) and unlike terms (different literal coefficients) with examples.
Definition and classification of algebraic expressions: monomial, binomial, trinomial, and polynomial expressions.
Definition of equations as statements of equality, illustrated with an example showcasing the left and right sides.
Summary of key concepts: coefficients, terms classifications, algebraic expressions, and equations.
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- 1. Algebra - Recap • In the last class you got to know about origin of Algebra. • You learned that algebra is mathematics of unknowns. • In algebra alphabets are used for denoting unknown numbers. • In algebra addition and subtraction are similar to previously learned in maths. In this class you will learn about new names that are used in algebra. Edishta Resource Centre www.edishta.com
- 2. Algebra – Class2 Terminologies used in Algebra 2 Edishta Resource Centre www.edishta.com
- 3. Algebra - AlgebraicTerms Let us call these newly known terms like 5x, 8xyz, 7i, 2jk and such terms with some name to use We call them as Algebraic Terms An algebraic term is that It should have a number and alphabets - 25, 3,-2, 8/7 are not algebraic terms. But x/7, 5z, 56/ pk, xy are Algebraic Terms. Edishta Resource Centre www.edishta.com
- 4. Algebra - Coefficient You observe closely these 4x, 6y, 3z, 10b etc. that are used in algebra… Do you see two separate parts in each one of them? One is number part i.e. 4, 6, 3, 10 and Another is unknown part which are x, y, z, b... Let’s name them.. Number part is called as Numerical Coefficient Unknown part is called as Literal Coefficient 4 Edishta Resource Centre www.edishta.com
- 5. Algebra - AlgebraicTerms With these new names let us define once again the Algebraic Terms So an Algebraic Term is Any numerical coefficient (number) with one or more than one literal coefficient (alphabets) Number (Numerical Coefficient) Alphabets (Literal Coefficient) Algebraic Term Edishta Resource Centre www.edishta.com
- 6. Algebra – Liken Unlike terms Observe 2x, 4x, 23x, 51x .. These algebraic terms are having similar literal coefficient i.e. x We call such similar looking algebraic terms as Like terms Example: 1) 5y, 9y, 13y It is having same coefficient y 2)4m, m, 2m, 18m Here coefficient is m for all 6 Like terms looks alike and similar Edishta Resource Centre www.edishta.com
- 7. Algebra - Liken Unlike terms 3x, 8y, 34c, 423z .. Are algebraic terms, having different coefficients x, y, c, z So we call such algebraic terms as Unlike terms 7 Example: 1) 2y, 19z, 23a These are having different coefficients 2) ma, 3a, 22c, 18x Here coefficients are not same for all Unlike terms looks differently Edishta Resource Centre www.edishta.com
- 8. Algebra - AlgebraicExpression Now we shall combine these algebraic terms When one or more than one algebraic terms are combined with ‘+’ or ‘–’ then it is called as Algebraic Expression Example: 4a, 2x + 3d, 9s, 2ks- xy+ 4mn, 2pr/n- yz/2, x +4 -y Are all called as algebraic expressions 30 – 5 , 832 + 23, 358/324 are not algebraic expressions All algebraic expression must contain at least one algebraic term Edishta Resource Centre www.edishta.com
- 9. Algebra - AlgebraicExpression Continuing with Algebraic expressions we can classify them based on number of algebraic terms present in them An algebraic expression with single algebraic term is Monomial Expressions Eg: 3x, 5c, 8b An algebraic expression with two algebraic term is Binomial Expressions Eg: 4x+4y, 3y – 4a, 9a + 10z With three algebraic terms an algebraic expression is called as Trinomial Expressions Eg: 34x + 4b + 9c, 8x – 32a + 4y Edishta Resource Centre www.edishta.com
- 10. Algebra - AlgebraicExpression Expression having more than three terms are Polynomial Expressions Eg: x + 3a - 8b + 5d, 3d +4s + 2a -5c + x Single term Monomial Two Terms Binomial Three terms Trinomial More than three terms Polynomial Edishta Resource Centre www.edishta.com
- 11. Algebra - Equation After expressions let us see new term Equation An equation says that two things are equal. It will have an equals sign "=" in between Ex: x + 2 = 6 That equation says: what is on the left (x + 2) is equal to what is on the right (6) So an equation is like a statement "this equals that" Or Left hand side (LHS) = Right hand side (RHS) 11 Edishta Resource Centre www.edishta.com
- 12. Algebra - Summary • Two parts of algebraic terms are Numerical and Literal Coefficient Literal Coefficient are equal Like Terms. Eg: 4a,6a, -2a,8a Literal Coefficient are not equal Unlike Terms. Eg: 3s, a, -x, 9b • Algebraic terms combined with + or – will form algebraic expression Single term Monomial Expression Eg: 3a, z,8x Two Terms Binomial Expression Eg: 8x+2a, 3y-3z Three terms Trinomial Expression Eg: 2x + 3y + z More than three terms Polynomial Expression Eg: 8x-a + 2c + 3y • An Equation is an statement like LHS = RHS Edishta Resource Centre www.edishta.com