Introduction to Algebra

Variable- It is an unknown quantity that changes according to the situation.
Example: In the expression 7x + 5, x is the variable.

Constant- It has a fixed value.

In the given example 7x + 5, 5 is the constant.

Terms of an Expression

Portions of an expression which are formed independently first and afterward added or deducted, are known as terms.
In the above-given example, terms 7x and 5 are added to form the expression \left( {7x + 5} \right).

Factors of a term

  • Factors of a term are quantities which cannot be further factorised.
  • In the above-given example, factors of the term 7x are 7 and x.

Coefficient of a term

The numerical factor of a term is called the coefficient of the term.
In the above-given example, 7 is the coefficient of the term 7x.

Like and Unlike Terms

Like terms

Terms having the similar variables are called like terms.
Example: 8xy and 3xy are like terms.

Unlike terms

Terms having different variables are called, unlike terms.
Example: 7xy and -3x are unlike terms.

Monomial, Binomial, Trinomial and Polynomial Terms

No. of terms123>3
Example5xy\left( {4x - 1} \right)\left( {2x + 8y - 2} \right)\left( {7x + 4yx - 3y + 6} \right)

Formation of Algebraic Expressions

Combinations of variables, constants and operators constitute an algebraic expression.

Example: 6x + 7,\;4y + 3xy, etc.

Addition and Subtraction of Algebraic Expressions

Addition and Subtraction of like terms

  • The Sum of two or more like terms is a like term.
  • Its numerical coefficient will be equal to the sum of the numerical coefficients of all the like terms.
  • The difference between two like terms is a like term.
  • Its numerical coefficient will be equal to the difference between the numerical coefficients of the two like terms.
    Addition and Subtraction of unlike terms
  • like terms of both the expressions are grouped together and unlike terms are retained as it is, for adding or subtracting two or more algebraic expressions.

Algebra as Patterns

Number patterns

Successor of a natural number is \left( {{\rm{n }} + {\rm{ }}1} \right),If a natural number is denoted by n.
Example: Successor of n = 10 is {\rm{n}} + 1 = 11.

If a natural number is denoted by n, then 2n is an even number and \left( {2{\rm{n}} + 1} \right)is an odd number.
Example: If n = 10, then 2n = 20 is an even number and 2{\rm{n}} + 1 = 21\;is an odd number.

Patterns in Geometry

Some geometrical figures follow patterns which can be represented by algebraic expressions.

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