Algebra is the branch of Mathematics in which we study & deal with not only numbers but also letters of English alphabets. Is it surprising to know that we deal with alphabets also in Mathematics? Does that mean that we can do mathematical operations also on these alphabets? There might be many such questions in your mind. But yes, it is true. In Algebra we do mathematical operations on both, th mathematical numbers & the English alphabets.
Till now we have learnt many formulae like while finding the Perimeter of rectangle , we learnt ; Perimeter of rectangle = 2 * ( l + b ) or more specifically , 2 * ( length + breadth ) . What is l & b in Mathematics? Can we add them & then multiply their sum also by 2 . No, the alphabets as such cannot be added . But by writing alphabets in some equations or expressions we mean that we can assign any value to them. Like in the formula for the perimeter of rectangle ; by l & b we mean that whatever rectangle we take for finding the perimeter , it has some length & some breadth , we just have to add both & multiply their sum by 2 . Thus, 2 * ( l + b ) is a generalised expression for finding the perimeter of any rectangle given its length & breadth .
Such values which do not have any fixed value like numbers are represented by letters & are called variables in algebra. They are so called as their value keeps varying with the given conditions. Also the numbers which have fixed value as always; are termed as constants which means fixed value, hence the term.
At the earlier levels of algebra 1 , we must know about the basics of algebra as all the definitions & concepts explained above , about algebraic expressions & their terms & also the different types of polynomials given here.
Having learnt what algebra is, let us know about algebraic expressions now. As in Arithmetic, expressions in algebra also involve the mathematical operations between different values available in algebra. As just learnt that we have fixed & variable values in algebra, so on joining these values with the mathematical operators, we get algebraic expressions. A few examples are 3x+8, 9/y, 7p-6, etc. Here in the expressions we note that some values are written together without any operator, as 3x in the 1stexpression & 7p in the third; we must note that the operator at such places is multiply.
When two or more values are combined using * or /, they are called terms of the algebraic expression & the terms are separated from each other with the help of + or -. There are some expressions with only 1 term as 9/y in the above examples. Such expressions are called monomials in algebra. If the number of terms in an expression is 2 or more, it is called a polynomial which can further be classified as binomial, trinomial or quadrinomial depending on whether it has 2, 3or 4 terms respectively. If the number of terms exceeds 4, it is simply called a polynomial.
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