An expression consisting of arithmetic numbers, letters (used as symbols) and operation signs is called an Algebraic Expression
2x + 3y , -9p + 2r, x2 + 5x + 6, a3 + b3 + 3ab2 + 3a2b
Algebraic symbols that have a fixed value and do not change like variables (which are used as place holders) are called Constants
In 2x + 3y + 4, 4 is a constant. In 2a2 – 3ab + 7, 7 is a constant
A symbol in Algebra that can be plugged in with different numerical values (numbers) is called a variable
In 5p + 6q + r, the letters (symbols) p,q are called Variables.
Note: 5p + 6q + r is also a variable, since any number can be plugged in for p, q and r as required.
4 .Terms of an expression
The parts in an algebraic expression connected by the
operation signs + or — are called Terms
In 2y + 3, 2y is one term and 3 is another term.
An algebraic expression containing only one term is called a Monomial. Monomials are also called simple expressions.
2x, 5x2 , pq are examples of monomials.
An algebraic expression that contains two terms is called a Binomial
2x + 3y, 2p2 + 9y3 are some examples of Binomials.
An algebraic expression that has three terms is called a Trinomial.
3x + 4y + 5z, ax2 + bx + c are examples of Trinomials.
An algebraic expression that contains one term, two terms, three terms or more is called a Polynomial.
By this definition, each of monomial, binomial and trinomial is a Polynomial.
Examples of Polynomials are:
3x, 4y2, pq, (which are Monomials)
3x + 4y, 5q + 9t, -m2 – n2 (which are Binomials)
ax2 + bx + c, 3a - b + (5/3) c. (which are Trinomials)
Symbols or Numbers in multiplication are called factors.
In pq, p and q are factors in the multiplication
p × q.
pq is called the product of the factors p and q.
2 and 3 are factors in the multiplication 2×3 which is equal
2 and 3 are called Numerical Factors
6 is called the product of 2 and 3.
In the product xy, x and y are the factors and xy is called the product of x and y.
x and y are called Literal Factors.
Coefficient is of two types. Numerical coefficient and Literal coefficient.
Numbers form Numerical coefficients and symbols form literal coefficients.
In 2xy, 2 is the number or the Numerical coefficient while xy, the symbol, is the Literal Coefficient.
In the Monomial y, the Numerical coefficient is 1 and the literal coefficient is y
In the product 100xy, 100 is the Numerical coefficient and xy is the literal coefficient.
11. Like Terms:
Two or more terms that have the same literal coefficients are called Like Terms. Like terms can have different Numerical Coefficients, but not literal coefficients.
4pq and 100pq are like terms as the literal coefficients xy are same in the two terms.
-13p2q2 and 13 p2q2 are Like terms as only the numerical coefficients are different but the literal coefficients are same.
12. Unlike Terms
Terms that are not Like terms are Unlike Terms.
So, Unlike terms have different literal coefficients.
3xy, 3xy2 are unlike terms