As we know the Algebra says an equation, an expression with variable.
Here we will know how algebraic expressions are formed, how they can be combined, how we can find their values and how they can be used.
An Algebraic expression must have a variable. A variable can take various values. The value of variables has not fixed, but while any variable has any fixed value than that's says constant.
Where a variable can any alphabets where as constant has a numeric value.
An algebraic expression has to form with combination of variables and constants.
With the algebraic expression we can form addition, subtractions, multiplications and also division.
Whenever we us of any rules there has to some rules, terms for that. How to use that, where can be use that etc.
In same of some of rules, terms have for Algebraic expressions. Here we will try to understand the terms of expression and their factors.
When have any expression with the minus sign (−) is included in the term. In the expression 4x2 −3xy, we took the term as (−3xy) and not as (3xy). That is why we do not need to say that terms are ‘added or subtracted’ to form an expression; just ‘added’ is enough.
When factors may be numerical and the others algebraic (i.e., they contain variables). The numerical factor is said to be the numerical coefficient or simply the coefficient of the term.
When we say that in the term 5xy, 5 is the coefficient of xy, x is the coefficient of 5y and y is the coefficient of 5x.
When terms have the same algebraic factors, they are like terms. When terms have different algebraic factors, they are unlike terms.
For example-
In the expression 2xy − 3x + 5xy − 4, look at the terms 2xy and 5xy. The factors of 2xy are 2, x and y. The factors of 5xy are 5, x and y.
An expression with only one term is called a monomial; for example, 7xy, − 5m, 3z2, 4 etc.
An expression which contains two unlike terms is called a binomial; for example, x + y, m − 5, mn + 4m, a2 − b2 are binomials. The expression 10pq is not a binomial; it is a monomial. The expression (a + b + 5) is not a binomial.
An expression which contains three terms is called a trinomial;
3x2 − 5x + 2, m + n + 10 are trinomials.
An expression with one or more terms is called a polynomial. Thus a monomial, a binomial and a trinomial are all polynomials.
The sum of two or more like terms is a like term with a numerical coefficient equal to the sum of the numerical coefficients of all the like terms.
Similarly, the difference between two like terms is a like term with a numerical coefficient equal to the difference between the numerical coefficients of the two like terms.
Note, unlike terms cannot be added or subtracted the way like terms are added or subtracted.
We know that the value of an algebraic expression depends on the values of the variables forming the expression. There are a number of situations in which we need to find the value of an expression, such as when we wish to check whether a particular value of a variable satisfies a given equation or not.
Putting x = 2
(i) In x + 4, we get the value of x + 4, i.e., x + 4 = 2 + 4 = 6
Perimeter formulas
The perimeter of an equilateral triangle = 3 x the length of its side. If we denote the length of the side of the equilateral triangle by l, then the perimeter of the equilateral triangle = 3l
Similarly, the perimeter of a square = 4l where l = the length of the side of the square.
Perimeter of a regular pentagon = 5l where l = the length of the side of the pentagon and so on.
Area formulas
If we denote the length of a square by l, then the area of the square = l 2
If we denote the length of a rectangle by l and its breadth by b, then the area of the rectangle = l x b = lb.
Similarly, if b stands for the base and h for the height of a triangle, then the area of the triangle =b * h/2 = bh/2.