Terms of an Expression
The parts of an expression which are formed separately first and then added are called terms. A term is a product of its factors. The numerical factor of a term is called the numerical coefficient or simply the coefficient of the term. When the coefficient of a term is +1, it is usually omitted.
Like and Unlike Terms
Terms having the same algebraic factors are called like terms while terms having different algebraic factors are called, unlike terms.
To decide whether the given terms are like or unlike terms, we follow the following simple steps:
- Ignore the numerical coefficients. Concentrate on the algebraic part of the terms.
- Check whether the variables in the terms are the same or not.
- Next, check whether the powers of each variable in the terms are same or not.
Note that in deciding like terms (i) the numerical coefficients of the terms and (ii) the order in which the variables are multiplied in the terms do not matter.
Addition and Subtraction of Like Terms
The sum (or difference) of two like terms is a like term with a coefficient equal to the sum (or difference) or the coefficients of the two like terms.
Monomial, Binomial, Trinomial and Polynomial Terms
Types of expressions based on the number of terms
Based on the number of terms present, algebraic expressions are classified as:
- Monomial: An expression with only one term.
Example: 7xy, −5m, etc. - Binomial: An expression which contains two, unlike terms.
Example: 5mn+4, x+y, etc - Trinomial: An expression which contains three terms.
Example: x+y+5, a+b+ab, etc.
Addition and Subtracting General Algebraic Expressions
When we add two algebraic expressions, the like terms are added; the unlike terms are left as they are.
Finding the Value of an Expression
The value of an algebraic expression depends on the values of the variables forming the expression. We need to evaluate an algebraic expression when we wish to check whether a particular value of a variable satisfies a given equation or not. Also, we find values of expressions, when we use formulae from geometry and from everyday mathematics.
Using Algebraic Expressions-Formulas and Rules
Perimeter Formulas
The perimeter of an equilateral triangle = 3l, where l is the length of the side of the equilateral triangle.
The perimeter of a square = 4l, where l is the length of the side of the square.
Area Formulas
Area of a square = l2, where l is the side of the square.
Area of a rectangle = l × b, where l and b are respectively length and the breadth of the rectangle.
Area of triangle = 1/2 b×h, where b is the base of the triangle and h is the height of the triangle.
Rules for Number Patterns
1. If a natural number is denoted by n, its successor is (n + 1).
2. If a natural number is denoted by n, 2n is an even number and (2n + 1) is an odd number.
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