Fundamental Concept of **Algebraic Expressions Class-8 RS** Aggarwal Solutions ICSE Mathematics Goyal Brothers Prakashan Chapter-12. We provide step by step Solutions of Exercise / lesson-12 **Sets** for **ICSE Class-8 RS** Aggarwal Mathematics.

Our Solutions contain all type Questions of Exe-12 A, Exe-12 B, Exe-12 C, Exe-12 D and Exe-12 E (MCQ) with Notes to develop skill and confidence. Visit official Website **CISCE** for detail information about ICSE Board Class-8 Mathematics.

## Fundamental Concept of **Algebraic Expressions Class-8 RS** Aggarwal Solutions ICSE Mathematics Goyal Brothers Prakashan Chapter-12

**–: Select Topics :–**

An algebraic expression in mathematics is an expression which is made up of variables and constants along with algebraic operations (addition, subtraction, etc.) Expressions are made up of terms. They are also termed as algebraic equations.Also,

These expressions are represented with the help of unknown variables, constants and coefficient. The combination of these three is said to be terms of expressions. It is to be noted that, unlike algebraic equation, an algebraic expression has no sides or equal to sign

### Variables, Coefficient & Constant

In Algebra we work with Variable, Symbols or Letters whose value is unknown to us.

## Types of Algebraic expression

There are 3 mains types of algebraic expressions which include:

- Monomial Expression
- Binomial Expression
- Polynomial Expression

### Monomial Expression

An algebraic expression which is having only one term is known as a monomial.

Examples of monomial expression include 3x^{4}, 3xy, 3x,8y, etc.

### Binomial Expression

A binomial expression is an algebraic expression which is having two unlikely terms.

Examples of binomial include 5xy + 8, xyz + x^{3}, etc.

### Polynomial Expression

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

Examples of polynomial expression include ab + bc + ca, etc.

## Other Types of Expression:

Apart from mononomial, binomial and polynomial types of expressions, algebraic expression can also be classified into two additional types which are:

- Numeric Expression
- Variable Expression

### Numeric Expression

A numeric expression consists of numbers and operations, but never include any variable. Some of the examples of numeric expressions are 10+5, 15÷2, etc.

### Variable Expression

A variable expression is an expression which contains variables along with numbers and operation to define an expression. A few examples of a variable expression include 4x+y, 5ab + 33, etc.

### Formulas

The general algebraic formulas we use to solve the expressions or equations are:

- (a+b)
^{2}= a^{2}+ 2ab + b^{2} - (a – b)
^{2}= a^{2}– 2ab + b^{2} - a
^{2}– b^{2}= (a – b)(a + b) - (a + b)
^{2}= a^{3}+ b^{3}+ 3ab(a + b) - (a – b)
^{2}= a^{3}– b^{3}– 3ab(a – b) - a
^{3}– b^{3}= (a – b)(a^{2}+ ab + b^{2}) - a
^{3}+ b^{3}= (a + b)(a^{2}– ab + b^{2})

**Exe-12-A** Fundamental Concept of **Algebraic Expressions Class-8 **

**RS** Aggarwal Solutions ICSE Mathematics Goyal Brothers Prakashan

#### Question 1:

Identify, monomials, binomial and trinomials from the following :

(i)……………

………………

#### Question 2:

Write the numerical and literal coefficient of each of the following terms:

(i)……………..

…………………..

#### Question 3:

……………………..

……………………

…………………….

#### Question 11:

State whether each of the following statements is true or false and rewrite the false statement after correcting them :

(i) 7x + y is the same as 7xy

(ii) 3x * 2p + 5q is a trinomial

…………………..

…………………..

**Exe-12-B** Fundamental Concept of **Algebraic Expressions Class-8 **

**RS** Aggarwal Solutions ICSE Mathematics Goyal Brothers Prakashan

#### Question 1:

Add :

(i) 2ab, -7ab, 2/3ab, 9ab

……………………

#### Question 2:

……………………

…………………….

…………………….

#### Question 10:

Subtract a³ – 3a² from b³ – 3b².

**Exe-12-C** Fundamental Concept of **Algebraic Expressions Class-8 **

**RS** Aggarwal Solutions ICSE Mathematics Goyal Brothers Prakashan

#### Question 1:

Multiply :

(i) 8x² by – 5x

(ii) 2/3 ab by – 6a²b

………………….

#### Question 3:

…………………….

…………………….

…………………..

#### Question 5:

Multiply :

(i) ………………….

………………………

**Exe-12- D** Fundamental Concept of **Algebraic Expressions Class-8 **

**RS** Aggarwal Solutions ICSE Mathematics Goyal Brothers Prakashan

#### Question 1:

Divide :

(i) ………………

(ii)……………..

……………………

#### Question 2:

………………….

…………………

………………….

#### Question 15:

Divide 6x^{4 }– 13x³ + 2x² + 22x – 24 by the product of 2x – 3 and x² – 2x + 2.

**Exe-12- E** Fundamental Concept of **Algebraic Expressions Class-8 **

**RS** Aggarwal Solutions ICSE Mathematics Goyal Brothers Prakashan

**Multiple Choice Questions**

**choose the correct option in each of the following:**

#### Question 1:

The coefficient of y² in -2/5 xy² z³ is

………………….

#### Question 2:

………………….

………………….

………………….

#### Question 12:

(x² – 4x + 4) + (x – 2) = ?

–: End of Fundamental Concept of **Algebraic Expressions ****RS Aggarwal** Solutions :–

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