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.

Algebraic Expression

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

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Practise This Question

Which of the following shows 114 and 258 on a number line?