Ch 9 covers multiplication of algebraic expressions (monomials, binomials, polynomials) and introduces the four standard algebraic identities. These identities are fundamental tools used throughout mathematics.
Monomial × monomial: multiply coefficients and add exponents of like variables. Monomial × polynomial: distribute (multiply each term). Polynomial × polynomial: multiply each term of one with every term of the other.
Identity I: (a+b)² = a² + 2ab + b². Identity II: (a−b)² = a² − 2ab + b². Identity III: (a+b)(a−b) = a² − b². Identity IV: (x+a)(x+b) = x² + (a+b)x + ab. These are true for all values of variables.
Identities help in quick multiplication (e.g., 99² = (100−1)² = 10000 − 200 + 1 = 9801), factorisation, and simplification of algebraic expressions.
Download: https://ncert.nic.in/textbook/pdf/hemh109.pdf | Complete book: https://ncert.nic.in/textbook/pdf/hemh1ps.zip
An algebraic identity is an equation that is true for all values of the variables involved. Unlike equations (true for specific values), identities hold universally. For example, (a+b)² = a² + 2ab + b² is always true.
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