0Key Points to Remember
1. Algebraic Expressions
Algebraic Expressions are formed from Variables and Constants.
The expression '2p–5' is formed from the variable 'p' and constants '2' and '5'. The expression '4xy+7' is formed from variables 'x' and 'y' and constants '4' and '7'.
Note that the value of expression changes in response to a change in the value of any of the variables that are part of the expression.
Thus as 'y' takes on different values, the value of the expression '2y–5' keeps changing.
In general, a Polynomial is an algebraic expression containing one or more terms with non-zero coefficients (with variables having non-negative integers as exponents).
'a+b+c+d', '3xy', '7xyz–10', '2x+3y+7z', etc., are a few examples for polynomials.
A Polynomial containing only one term is also referred to as a Monomial; one containing two terms is also referred to as a Binomial; one containing three terms is also referred to as Trinomial, and so on.
2. Terms, Factors and Coefficients
All (Algebraic) Expressions comprise of one or more Terms added together.
For instance, the algebraic expression '4v+9' is the sum of two 'terms' viz., '4v' and '9'. On the same lines, '8xy+6z-2' is the sum of three terms '8xy', '6z' and '-2' respectively.
Terms themselves are the product of Factors.
So, in the example expression '4v+9' above, the term '4v' is a product of factors '4' and 'v' while the second term '9' is made up of a single factor '9'.
The non-zero numerical factor of a Term is referred to as Coefficient or Numerical Coefficient.
So, in the expression '8xy+6z-2' the coefficient in the term '8xy' is '8', the coefficient in the term '6z' is '6' and the coefficient in the term '-2' is '-2'.
3. Like vs Unlike Terms
Terms that share identical, non-numerical factors between them are referred to as Like Terms. Terms that don't do so are referred to as, Unlike Terms.
Examples:
- '5x', '10x', and '-23x' all share the same non-numerical factor 'x'. So they are like terms
- '5yz' and '-4yz' contain identical non-numerical factor 'yz' and so, are like terms
- Point to note, '7xy' and '-5yx' are like terms too, since xy=yx
In the next part of the lesson, we shall be learning Addition and Subtraction of Polynomials. Ensure the concepts discussed here are well understood before moving on to the next part.
I wish you great learning!
