What is algebraic expression?
The combination of constants and variables, connected by signs of fundamental operations (+, -, ×, ÷) is called an algebraic expression.
2x – 3y + 9z is an algebraic expression.
In the algebraic expression 3x² + 7y³ - 4xy.
3x², 7y³, -4xy are called terms of the expression.
Classification of algebraic expressions Monomial: An algebraic expression containing only one term is called a monomial.
For example; 3x, -7, ⁵/₉ a²bc are all monomials.
Binomial: An algebraic expression containing two terms is called a binomial.
For example; x – 7, 5x + 9y, ab + care all binomials.
Trinomial: An algebraic expression containing three terms is called a trinomial.
For example; x – y + 7, 3x + 4y – 5z, a³ + b² + c⁴ are all trinomials.
Multinomial: An algebraic expression containing two term is called a multinomial.
For example; x³ y² + 2x²y – 3xy + 7, a² + b² - 4c² - d², l + m + n – p are all multinomials.
Polynomial: In an algebraic expression, if the power of variables is a non-negative integer; then that expression is called a polynomial.
For example; 3x² + 4x + 7 is a polynomial.
x² + 3x
is not a polynomial.
[The power of x in 3x
is negative. Therefore, 3x = 3x−1 ]
5√x + 2x² - 5 is not a polynomial.
[The power of x in 5√x is in fraction. Therefore, 5√x = 5x12
]
The combination of constants and variables, connected by signs of fundamental operations (+, -, ×, ÷) is called an algebraic expression.
2x – 3y + 9z is an algebraic expression.
In the algebraic expression 3x² + 7y³ - 4xy.
3x², 7y³, -4xy are called terms of the expression.
Monomial: An algebraic expression containing only one term is called a monomial.
For example; 3x, -7, ⁵/₉ a²bc are all monomials.
Binomial: An algebraic expression containing two terms is called a binomial.
For example; x – 7, 5x + 9y, ab + care all binomials.
Trinomial: An algebraic expression containing three terms is called a trinomial.
For example; x – y + 7, 3x + 4y – 5z, a³ + b² + c⁴ are all trinomials.
Multinomial: An algebraic expression containing two term is called a multinomial.
For example; x³ y² + 2x²y – 3xy + 7, a² + b² - 4c² - d², l + m + n – p are all multinomials.
Polynomial: In an algebraic expression, if the power of variables is a non-negative integer; then that expression is called a polynomial.
For example; 3x² + 4x + 7 is a polynomial.
x² + 3x
is not a polynomial.
[The power of x in 3x
]
5√x + 2x² - 5 is not a polynomial.
[The power of x in 5√x is in fraction. Therefore, 5√x = 5x12
]
