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

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.

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

---

-: Select Topics :-

Exercise-3(a)

Exercise-3(b)

Chapter Test

---

Exercise-3

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.

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.

Binomial Expansion :

Important points to remember

• The total number of terms in the expansion of (x+y)ⁿ  are (n+1)
• The sum of exponents of x and y is always n.
• nC₀, nC₁, nC₂, … .., nC_n are called binomial coefficients and also represented by C₀, C₁, C2, ….., C_n
• The binomial coefficients which are equidistant from the beginning and from the ending are equal i.e. nC₀ = nC_n, nC₁ = nC_n-1 , nC₂ = nC_n-2 ,….. etc.

Properties of Binomial Coefficients :

Binomial coefficients refer to the integers which are coefficients in the binomial theorem. Some of the most important properties of binomial coefficients are:

• C₀ + C₁ + C₂ + … + C_n = 2ⁿ
• C₀ + C₂ + C₄ + … = C₁ + C₃ + C₅ + … = 2^n-1
• C₀ – C₁ + C₂ – C₃ + … +(−1)ⁿ . nC_n = 0
• nC₁ + 2.nC₂ + 3.nC₃ + … + n.nC_n = n.2^n-1
• C₁ − 2C₂ + 3C₃ − 4C₄ + … +(−1)^n-1 C_n = 0 for n > 1
• C₀² + C₁² + C₂² + …C_n² = [(2n)!/ (n!)²]

Terms in the Binomial Expansion :

In binomial expansion, it is often asked to find the middle term or th general term. Here, the different terms in the binomial expansion that are covered here include:

• General Term
• Middle Term
• Independent Term
• Determining a Particular Term
• Numerically greatest term
• Ratio of Consecutive Terms/Coefficients

---

Exercise-3.(a)

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

Question 1:

Write down the products for each of the following :

(i)………

(ii)……….

(iii)……….

(iv)…………

Question 2:

Write down the square of the following expressions

(i)………

(ii)……….

(iii)……….

(iv)…………

(v)……………..

(vi) …………….

Question 3:

Simplify :

…………………………

……………………….

……………………….

Question 9:

Write down the expansion of the following :

(i)………

(ii)……….

(iii)……….

(iv)…………

(v)……………..

---

Exercise-3.(b)

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

Question 1:

Find the value of :

(i)………

(ii)……….

(iii)……….

(iv)…………

(v)……………..

Question 2:

…………………………..

………………………….

……………………………..

Question 5:

Evaluate :

(i)………

(ii)……….

(iii)……….

---

Chapter Test

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

Question 1:

The coefficient of x in the product (2-3x) (5 – 2x) is….

Question 2:

If ………………… value of k is :

Question 3:

The coefficient …………………..

Question 4:

…………………

………………….

…………………

Question 8:

If (a-1)² ………………… is ………

Question 9:

If ax + by + = 3, …………………………… a² + b² is

Question 10:

If p + q = 10 …………………… q/p will be :

— : End of Expansions  OP Malhotra S Chand Solutions :–

---

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

Thanks

Please Share with Your Friends