# Algebraic Expressions

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,  4×3-10 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. $$3x^{4}, 3xy$$ etc.

(ii)

## Binomial

: Expression having two unlikely terms are known as binomial.

Eg. 5xy + 8,  $$xyz + x^{3}$$ etc.

(iii)

## Polynomial

: In general an expression with more than one terms with non-negative integral exponents of variable is known as Polynomial.

Eg. $$ab + bc + ca$$ etc.

Types of Expression:

(i) Numeric Expression: Consist of numbers and operations, but never include any variable.

Eg. 10+5,  $$15 \div 2$$, etc.

(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:

 S.no Term Simplification Type of Expression 1 $$3xy^{3} +9x^{2}y^{3} + 5y^{3}x$$ $$8xy^{3}+9x^{2}y^{3}$$ Binomial 2 $$7ab^{2}c^{2} + 2 a^{3}b^{2} -3 abc – 5ab^{2}c^{2} – 2b^{2}a^{3} + 2ab$$ $$2ab^{2}c^{2} -3 abc + 2ab$$ Trinomial 3 $$50x^{3} – 20x +83 + 21 x^{3} – 3x + 3 + 15x – 86 – 41x^{3} + 8x$$ $$30x^{3}$$< Monomial