# CLASS-6ALGEBRA -TRINOMIAL

TRINOMIAL -

In algebra, a trinomial is an algebraic expression or polynomial that consists of exactly three unlike terms connected by addition or subtraction. Trinomials are a common type of polynomial and are used to represent various mathematical relationships and equations. Here are some key characteristics and examples of trinomials:

1. Three Terms:- A trinomial is composed of exactly three terms, and each term can be a combination of constants, variables, and exponents.
2. Unlike Terms:- The three terms in a trinomial must be different from each other. They may differ in variables, exponents, or constants.
3. Operator:- The terms in a trinomial are connected by either addition (+) or subtraction (-) operators.

Examples of Trinomials:-

1. Quadratic Trinomial:- "2x²+ 5x - 3" is a trinomial consisting of three unlike terms connected by addition. The first term is "2x²" (a quadratic term involving the variable "x" raised to the second power), the second term is "5x" (a linear term), and the third term is "-3" (a constant).
2. Constant Trinomial:- "4 - 2 + 7" is a trinomial consisting of three constant terms connected by both addition and subtraction operators.
3. Mixed Trinomial:- "3y³- 2y + 1" is a trinomial consisting of three unlike terms connected by both addition and subtraction operators. The terms involve variables "y" and constants.
4. Variable Trinomial:- "a²- b²+ ab" is a trinomial consisting of three terms, two of which involve variables "a" and "b." The terms are connected by subtraction and addition operators.

A trinomial is an algebraic expression that has three non-zero terms.

Examples of a trinomial expression (Another way Of Understanding):-

·   x + y + z is a trinomial in three variables x, y and z.

·   2a²+ 5a + 7 is a trinomial in one variables a.

·   xy + x + 2y² is a trinomial in two variables x and y.

·   -7m⁵ + n³– 3m²n² is a trinomial in two variables m and n.

·   5abc – 7ab + 9ac is a trinomial in three variables a, b and c.

·   x²/3 + ay – 6bz is a trinomial in five variables a, b, x, y, and z.

Trinomials are essential in algebra for solving equations, factoring, and representing various mathematical relationships. They can be manipulated, simplified, and combined with other expressions to create more complex algebraic expressions or equations. Understanding trinomials is crucial for algebraic problem-solving and modeling.