An algebraic expression is a branch of Mathematics made up of variables and constants along with operations(addition, subtraction, etc.)
Expressions are made up of terms.
Example of algebraic expression:
3x+4y 7, 4×310 etc.
It is to be noted that, an expression has no sides or equal to sign, just like in algebraic equation.
The terminology used in Algebraic expressions:
In Algebra we work with Variable, Symbols or Letters whose value is unknown to us.
In the above expression, x is a Variable, whose value is unknown to us which can take any value.
5 is known as Coefficient of x, as it is a constant value used with the variable term and is well defined.
3 is the Constant value term which has a definite value.
The whole expression is known to be the Binomial term, as it has two unlikely terms.
Types of Algebraic expression:
(i)
Monomial
: Algebraic expression having one term is know as monomial. Eg. \(3x^{4}, 3xy\)
(ii)
Binomial
: Expression having two unlikely terms are known as binomial.
Eg. 5xy + 8, \(xyz + x^{3}\)
(iii)
Polynomial
: In general an expression with more than one terms with nonnegative integral exponents of variable is known as Polynomial.
Eg. \(ab + bc + ca\)
Types of Expression:
(i) Numeric Expression: Consist of numbers and operations, but never include any variable.
Eg. 10+5, \(15 \div 2\)
(ii) Variable Expression: These contains variables along with numbers and operation to define an expression.
Eg. 4x+y, 5ab+33, etc.
Example: Simplify the given expressions by combining the like terms and write the type of Algebraic expression. (i) \(3xy^{3} +9x^{2}y^{3} + 8x^{3} + 5y^{3}x\) (ii) \(7ab^{2}c^{2} + 2 a^{3}b^{2} 3 abc – 5ab^{2}c^{2} – 2b^{2}a^{3} + 2ab\) (iii) \(50x^{3} – 20x +83 + 21 x^{3} – 3x + 3 + 15x – 41x^{3}\) Solution: Creating a table to find the solution:

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