Chapter 8 — Algebraic Expressions and Identities

Chapter 8 of the Class 8 Maths NCERT textbook, "Algebraic Expressions and Identities", teaches how to add, subtract, and multiply algebraic expressions including monomials, binomials, trinomials, and polynomials using the distributive law and rules of exponents.

• Combining like terms — Addition and subtraction of expressions rest on identifying like terms — same variables to the same powers — and combining their coefficients, the foundation for all later manipulation.
• Multiplying expressions — The distributive law drives multiplication from monomial-by-polynomial up to binomial-by-trinomial, where each term multiplies each other term and the results are simplified by collecting like terms.
• Same laws, real uses — Algebraic operations obey the same commutative, associative and distributive laws as numbers, and the chapter grounds them in areas, volumes and pricing problems.

1. 01Like terms have the same variables with the same powers; add or subtract them by combining coefficients
2. 02Monomial: expression with exactly one term; multiply two monomials by multiplying coefficients and combining variable powers using exponent rules
3. 03Distributive law: multiply a monomial by a polynomial by distributing the monomial to each term in the polynomial
4. 04Binomial × binomial: each term in one binomial multiplies each term in the other; combine like terms in the result
5. 05Binomial × trinomial produces 6 terms initially (2 × 3) that may reduce when like terms are combined
6. 06All algebraic operations (addition, subtraction, multiplication) follow the same laws as number operations (commutative, associative, distributive)
7. 07Real-world applications: area of rectangle = length × breadth, volume of box = length × breadth × height, cost = price × quantity