Chapter 8 – Division of Algebraic Expressions
RD Sharma Class 8 Maths Chapter 8 – Division of Algebraic Expressions
Division of RD Sharma Algebraic Expressions is an important chapter in Class 8 Mathematics that strengthens your understanding of algebraic operations. This chapter focuses on dividing algebraic expressions using systematic methods, simplifying expressions, and applying factorisation. Mastering this topic helps students build a strong foundation for higher-level algebra.
Find the PDF Solutions of all the exercises in Chapter 8 – Division of Algebraic Expressions
Introduction to Algebraic Division
RD Sharma class 8 Solutions for Algebraic expressions consist of variables, constants, and mathematical operations such as addition, subtraction, multiplication, and division. Division of algebraic expressions involves finding how many times one algebraic expression is contained within another.
This process is similar to numerical division but requires careful handling of variables and exponents. Students must understand the rules of exponents and factorisation before solving problems from this chapter.
Key Concepts Covered
1. Division of Monomials
A monomial is an algebraic expression with only one term. Dividing monomials involves dividing the coefficients and subtracting the exponents of like variables.
Example:
(12x³) ÷ (3x) = 4x²
Steps:
- Divide coefficients: 12 ÷ 3 = 4
- Subtract exponents: x³ ÷ x = x²
This method is straightforward and forms the basis for more complex problems.
2. Division of a Polynomial by a Monomial
When dividing a polynomial by a monomial, each term of the polynomial is divided separately.
Example:
(8x² + 4x) ÷ 2x
= (8x² ÷ 2x) + (4x ÷ 2x)
= 4x + 2
This method uses the distributive property and ensures each term is simplified properly.
3. Division of Polynomials
Dividing one polynomial by another requires a structured approach. There are two main methods:
a) Factorisation Method
This method involves factoring both the dividend and divisor and then canceling common factors.
Example:
(x² – 9) ÷ (x – 3)
= (x – 3)(x + 3) ÷ (x – 3)
= x + 3
b) Long Division Method
This method is used when factorization is not straightforward.
Steps include:
- Arrange terms in descending order
- Divide the first term
- Multiply and subtract
- Repeat until completion
This method is similar to long division in arithmetic.
4. Division Using Identities
Algebraic identities simplify division problems significantly. Some important identities include:
- a² – b² = (a – b)(a + b)
- (a + b)² = a² + 2ab + b²
Using these identities helps break down complex expressions into simpler factors, making division easier.
5. Simplification of Algebraic Fractions
Algebraic fractions are expressions where numerator and denominator are polynomials. Simplification involves:
- Factorizing numerator and denominator
- Cancelling common terms
Example:
(2x² + 4x) ÷ (2x)
= 2x(x + 2) ÷ 2x
= x + 2
Important Tips for Solving Problems
- Always factorize expressions before attempting division
- Check for common factors in numerator and denominator
- Apply exponent rules carefully
- Arrange polynomials in descending order for long division
- Double-check calculations to avoid sign errors
Common Mistakes to Avoid
Students often make errors while dividing algebraic expressions. Some common mistakes include:
- Incorrect subtraction of exponents
- Skipping factorization steps
- Ignoring negative signs
- Not simplifying completely
Avoiding these mistakes ensures accuracy in solving problems.
Importance of This Chapter
This chapter plays a crucial role in understanding advanced algebra topics such as rational expressions, equations, and polynomials. It also enhances logical thinking and problem-solving skills.
Students preparing for school exams or competitive tests will find this chapter extremely useful, as algebra forms a core part of mathematics.
Practice Strategy
To master division of algebraic expressions:
- Start with simple monomial divisions
- Practice polynomial division regularly
- Solve examples from textbooks thoroughly
- Revise algebraic identities frequently
- Attempt different types of problems
Consistent practice helps in building confidence and speed.