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Mathematics Class 8 - Algebraic Expressions-And-Identities Notes

Comprehensive study notes for Class 8 - Algebraic Expressions-And-Identities olympiad preparation

Algebraic Expressions and Identities

Welcome to the chapter on Algebraic Expressions and Identities for Class 8. In this chapter, you will learn about algebraic expressions, how to form and simplify them, and how to use identities to solve problems. By the end of this chapter, you will be able to work confidently with expressions and apply important algebraic identities!

Introduction

Algebraic expressions are combinations of numbers, variables, and mathematical operations. Identities are equations that are true for all values of the variables.

What is an Algebraic Expression?

An algebraic expression is made up of variables (like x, y), numbers, and operations (+, -, ×, ÷).

  • Example: 2x + 3y - 5
  • Example: a2 + 2ab + b2

Types of Algebraic Expressions

  • Monomial: An expression with one term (e.g., 5x).
  • Binomial: An expression with two terms (e.g., x + y).
  • Trinomial: An expression with three terms (e.g., x2 + 2x + 1).
  • Polynomial: An expression with more than one term.

Forming Algebraic Expressions

You can form expressions using variables and numbers to represent real-life situations.

  • Sum of a number x and 5: x + 5
  • Product of a and b: ab
  • Twice a number y: 2y

Simplifying Expressions

Combine like terms and use basic operations to make expressions simpler.

  • Example: 3x + 4x = 7x
  • Example: 2a + 5b - a = a + 5b

Algebraic Identities

Identities are formulas that are always true for any value of the variables.

  • (a + b)2 = a2 + 2ab + b2
  • (a - b)2 = a2 - 2ab + b2
  • (a + b)(a - b) = a2 - b2

Using Identities

Identities help us to expand, factorize, and simplify algebraic expressions quickly.

  • Expand (x + 3)2 using the identity: x2 + 6x + 9
  • Factorize x2 - 9 using the identity: (x + 3)(x - 3)

Fun Activity: Identity Match!

Write down different algebraic expressions and match them with the correct identity. Try expanding and factorizing them!

Summary

  • Algebraic expressions use variables, numbers, and operations.
  • Identities are formulas true for all values of variables.
  • Use identities to expand and factorize expressions easily.

Practice Questions

  1. Simplify: 4x + 7x
  2. Expand: (a + 2)2
  3. Factorize: y2 - 16
  4. Write an expression for "three times a number n minus 5".
  5. State the identity for (a - b)2.

Challenge Yourself

  • Expand (x - 4)2 using the identity.
  • Factorize x2 - 25.

Did You Know?

  • Algebra was first used by ancient mathematicians in India and the Middle East!
  • Identities make solving big algebra problems much faster.

Glossary

  • Variable: A letter that stands for a number.
  • Expression: A combination of numbers, variables, and operations.
  • Identity: An equation true for all values of the variables.
  • Expand: To multiply out and write as a sum.
  • Factorize: To write as a product of factors.

Answers to Practice Questions

  1. 11x
  2. a2 + 4a + 4
  3. (y + 4)(y - 4)
  4. 3n - 5
  5. (a - b)2 = a2 - 2ab + b2

Practice algebraic expressions and identities to become a math expert!

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