OP Malhotra Expansions Class-9 S.Chand ICSE Maths Ch-3. We Provide Step by Step Answer of Exe-3(a), Exe-3(b), with Chapter Test of S Chand OP Malhotra Maths . Visit official Website CISCE  for detail information about ICSE Board Class-9.

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OP Malhotra Expansions Class-9 S.Chand ICSE Maths Ch-3

Expansion :

Expansion is the act of expanding, mathematically speaking, it is removing all the brackets present in the expression. Usually in Maths, we encounter a few expressions where they place two sets of two terms, both in brackets side by side like this (a + b)(a – b). This requiring removing brackets and simplification.

Special Products 

1. (i) (a+b)² = a²+b²+2ab           (ii) (a-b)² = a²+b²-2ab
(iii) (a+b)² + (a-b)² = 2(a²+b²)        (iv) (a+b)² – (a-b)² = 4ab
(v) (a+b) (a-b) = a² – b²

2. (i) [a+(1/a)]² = a²+(1/a²)+2        (ii) [a-(1/a)]² = a²+(1/a²)-2
(iii) [a+(1/a)] [a-(1/a)] = a²+(1/a²)        (iv) [a+(1/a)]²+[a-(1/a)]² = 2 [a²+(1/a)²]
(v) [a+(1/a)]² –  [a-(1/a)]²  = 4

3. (a+b+c)² = a²+b²+c²+2(ab+bc+ca)

4. (i) (x+a)(x+b) = x²+(a+b)x+ab        (ii) (x-a)(x+b) = x²-(a-b)x-ab
(iii) (x+a)(x-b) = x²-(b-a)x-ab            (iv) (x-a)(x-b) = x²-(a+b)x+ab

Practice Questions by Using Formulas :-  Exe-3A

Binomial Theorem

As the power increases the expansion becomes lengthy and tedious to calculate. A binomial expression that has been raised to a very large power can be easily calculated with the help of Binomial Theorem.

Introduction to the Binomial Theorem :

The Binomial Theorem is the method of expanding an expression which has been raised to any finite power. A binomial Theorem is a powerful tool of expansion, which has application in Algebra, probability, etc.

More Identities

1. (a+b)³ = a³ + b³ + 3ab (a+b)
2. [a + (1/a)]³ = a³ + (1/a³) + 3 {a+(1/a)}
3. (a-b)³ = a³ – b³ – 3ab (a-b)
4. [a – (1/a)]³ = a³ – (1/a³) – 3 {a-(1/a)}
5. (a+b) (a²-ab+b²) = a³ + b³
6. (a-b) (a²+ab+b²) = a³ – b³
7. (a+b+c) (a²+b²+c²-ab-bc-ac) = a³ + b³ + c³ – 3abc

Practice Questions by Using More Identities :-  Exe-(3B)

In this chapter, we study all the topics on Compound Interest and do some practice questions also. Here we solve extra practice questions on this chapter for better understanding.

Here is the link for extra practice questions on Expansions :- Ch-Test

Return to :–   OP Malhotra S Chand Solutions for ICSE Class-9 Maths

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