Class 8 Maths - ICSE
Identities (ICSE)
The chapter 'Identities' in Class 8 ICSE Mathematics introduces students to algebraic equalities that hold true for every value of the variables involved. Building upon basic algebraic expressions, this chapter focuses on standard algebraic identities such as the square of a sum, square of a difference, and the product of the sum and difference of two terms. Mastering these identities is crucial as they simplify complex algebraic calculations, speed up mental math, and form the absolute foundation for factorization, quadratic equations, and advanced algebra in higher ICSE board classes.
Start Learning FreeKey Concepts
Algebraic Identity
An algebraic identity is an equality that is true for all values of the variables used in it, unlike a conditional equation which is true only for specific values.
Square of a Sum (a + b)^2
This identity states that the square of the sum of two terms equals the sum of the square of the first term, twice the product of the two terms, and the square of the second term.
Square of a Difference (a - b)^2
This identity shows that the square of the difference of two terms equals the sum of the square of the first term and the square of the second term, minus twice their product.
Product of Sum and Difference (a + b)(a - b)
This identity reveals that the product of the sum and difference of two terms is simply the difference of their individual squares.
Geometric Visualization
Identities can be visually understood and proved by calculating the areas of rectangles and squares split into smaller geometric regions.
Important Formulas
Board Exam Info
In the ICSE Class 8 Mathematics examination, this chapter typically carries around 6 to 10 marks. Common question types include direct expansion using identities, evaluating numerical expressions using suitable identities (e.g., calculating 102^2 as (100 + 2)^2), and finding the value of expressions like x^2 + 1/x^2 given the value of x + 1/x.
Frequently Asked Questions
What is the difference between an algebraic identity and an algebraic equation?
An identity is true for any value of the variables, whereas an equation is true only for specific values called solutions or roots.
How can I use identities to solve mental math problems like 98 squared?
You can write 98 as (100 - 2) and apply the identity (a - b)^2 = a^2 - 2ab + b^2 to calculate it easily as 10000 - 400 + 4 = 9604.
Why do we get a middle term '2ab' in the expansion of (a + b)^2?
When you multiply (a + b) by (a + b) using distributive law, you get a^2 + ab + ba + b^2. Since ab equals ba, they combine to give 2ab.
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