Chapter 4 of Class 9 Maths Ganita Manjari Part 1 is Exploring Algebraic Identities. It covers standard algebraic identities that hold true for all values of the variables involved, and shows how they speed up expansion, factorisation, and calculation. These Class 9 Mathematics Chapter 4 solutions are also useful as quick revision notes before exams.
What Is an Algebraic Identity?
An algebraic identity is an equation that is true for all values of the variables involved (unlike an equation that is only true for specific values).
Standard Identities
- (a + b)² = a² + 2ab + b²
- (a − b)² = a² − 2ab + b²
- a² − b² = (a + b)(a − b)
- (x + a)(x + b) = x² + (a + b)x + ab
- (a + b)³ = a³ + b³ + 3ab(a + b)
- (a − b)³ = a³ − b³ − 3ab(a − b)
- a³ + b³ = (a + b)(a² − ab + b²)
- a³ − b³ = (a − b)(a² + ab + b²)
Using Identities for Quick Expansion
Identities let us expand expressions like (2x + 3y)² quickly by substituting a = 2x, b = 3y directly into the standard form, instead of multiplying term by term.
Using Identities for Factorisation
Identities work both ways: they can also be used to factorise expressions. For example, x² − 9 = x² − 3² = (x + 3)(x − 3), using the difference of squares identity in reverse.
Using Identities for Mental Calculation
Identities can simplify arithmetic too — e.g. 102 × 98 = (100 + 2)(100 − 2) = 100² − 2² = 10000 − 4 = 9996, avoiding direct multiplication.
Class 9 Mathematics Chapter 4 – Notes and Extra Questions
Along with these NCERT Solutions, students can also use the Class 9 Mathematics Chapter 4 Extra Questions and Class 9 Mathematics Chapter 4 Revision Notes for quick revision and extra practice.
