Algebraic Expression Definitions

 

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1. Algebraic Expression:

An expression consisting of arithmetic numbers, letters (used as symbols) and operation signs is called an Algebraic Expression

Examples:
2x + 3y , -9p + 2r, x2 + 5x + 6, a3 + b3 + 3ab2 + 3a2b

2. Constant:

Algebraic symbols that have a fixed value and do not change like variables (which are used as place holders) are called Constants

Examples:
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In 2x + 3y + 4, 4 is a constant. In 2a2 – 3ab + 7, 7 is a constant

3. Variable

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.

5. Monomials

An algebraic expression containing only one term is called a Monomial. Monomials are also called simple expressions.
2x, 5x2 , pq are examples of monomials.

6. Binomial

An algebraic expression that contains two terms is called a Binomial
2x + 3y, 2p2 + 9y3 are some examples of Binomials.

7. Trinomial

An algebraic expression that has three terms is called a Trinomial.
3x + 4y + 5z, ax2 + bx + c are examples of Trinomials.

8. Polynomial

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)

9. Factor:

Symbols or Numbers in multiplication are called factors.

Example:

In pq, p and q are factors in the multiplication p × q.
pq is called the product of the factors p and q.

Example:

2 and 3 are factors in the multiplication 2×3 which is equal to 6.
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.

10. Coefficient:

Coefficient is of two types. Numerical coefficient and Literal coefficient.
Numbers form Numerical coefficients and symbols form literal coefficients.

Examples:

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.

Examples:

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.

Examples
3xy, 3xy2 are unlike terms