Concise Mathematics Class 8 ICSE Solutions for Chapter 11 - Algebraic Expressions

Mathematics has been classified into several different branches. The division that looks after numbers and their processes is known as arithmetic. It is utilized for numerical calculations like subtraction, addition, division, and multiplication. Geometry is known for the shapes and sizes of figures and their construction using a ruler, compass and pencil. Algebra is another intriguing branch in the shape of numbers and letters called variables we describe in our daily life.

Algebraic expressions comprise of variables and numbers alongside operational signs. Examples - subtraction, addition, exponentiation, multiplication with the division and natural exponent. Dividing with variables in an algebraic equation is known as fractional expression.

Numbers that could be put down in the fractional form are called rational numbers. Examples- Integers, terminating decimals and repeating decimals.

In case, an algebraic expression has the root of the fractional power or the variable with a variable base then the expression is known as an irrational expression.

Maybe, it is rational and irrational to make use of algebraic terms. Rational expressions are classified as integral and fractional expressions.

We need to comprehend the concept of expressions and equations to get a grip on mathematics.

Definition of Expression:

An expression from a mathematical point of view is something which consists of numbers, variables and an arithmetic operation between them. For example, (4m+ 5) is an expression in which the terms 4 and 5 are constant and the term m is a variable in the aforementioned expression and is separated by the arithmetic operation + (plus).

A variable does not have a fixed value. Generally, expression variables are represented by letters such as a, b, c, m, n, p, x, y, z, etc. We can create a lot of expressions by merging various variables and numbers.

How to Simplify the Algebraic Expressions?

The goal behind simplifying the algebraic expression is to seek the simplified term of the given expression. To simplify algebraic expression, we should first understand how to merge the same terms, order of operations, how to factor a number, to factor the expression or simplify it. The variables with the same degree are collected in conjunction with the same terms and the constant terms are separated for the process of simplification.

What is an Algebraic Expression?

An algebraic expression in mathematics is an expression composed of variables and constants with algebraic operations such as subtraction, addiction etc.

Terminology Used In Algebraic Expressions:

An expression consisting of operation symbols, variables, and numbers is called an algebraic expression. In Algebra we deal with parameters, symbols, or letters, the meaning of which we do not know.

Types of Algebraic expression:

The main types of algebraic terms are: 

• Monomial Expression.

• Binomial Expression.

• Trinomial Expression.

• Polynomial Expression.

Monomial Expression:

 An algebraic expression that has only one term is known as a monomial expression. 

Binomial Expression:

An algebraic expression that has two improbable terms is called a binomial expression.

Trinomial Expression:

An algebraic expression consisting of just three non-zero terms is called a trinomial.

Polynomial Expression:

Generally, an expression with a variable's non-negative integral exponents is defined as a polynomial.

Different Types of Expression:

An algebraic expression can also be classified into two different forms apart from monomial, binomial, and polynomial expressions:

1. Numeric Expression.

2. Variable Expression.

Numeric Expression:

Numbers and operations consist of a numerical expression but never have any element.

Variable Expression:

A variable expression is an expression that makes use of variables to describe an expression along with numbers and operations.