मराठी

Expand the expression: (1– 2x)5

Advertisements
Advertisements

प्रश्न

Expand the expression: (1– 2x)5

बेरीज
Advertisements

उत्तर

By using Binomial Theorem, the expression (1– 2x)5 can be expanded as

`(1– 2x)^5`

= `""^5C_0  (1)^5  -  ^5C_1  (1)^4  (2x)  + ^5C_2  (3)^3  (2x)^2  -  ^5C_3  (1)^1  (2x)^4  - ^5C_5  (2x)^5`

`1 - 5 (2x) + 10(4x^2) - 10  (8x^3) + 5 (16x^4) - (32x^5)`

= `1 - 10x + 40x^2  -  80x^3 + 80x^4  - 32x^5`

shaalaa.com
  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
पाठ 7: Binomial Theorem - EXERCISE 7.1 [पृष्ठ १३२]

APPEARS IN

एनसीईआरटी Mathematics [English] Class 11
पाठ 7 Binomial Theorem
EXERCISE 7.1 | Q 1. | पृष्ठ १३२

व्हिडिओ ट्यूटोरियलVIEW ALL [1]

संबंधित प्रश्‍न

Expand the expression (1– 2x)5


Expand the expression: `(x/3 + 1/x)^5`


Using Binomial Theorem, evaluate of the following:
(102)5


Using binomial theorem, evaluate the following:

(99)5


Using Binomial Theorem, indicate which number is larger (1.1)10000 or 1000.


Find (a + b)4 – (a – b)4. Hence, evaluate `(sqrt3 + sqrt2)^4 - (sqrt3 - sqrt2)^4`


Find (x + 1)6 + (x – 1)6. Hence or otherwise evaluate `(sqrt2 + 1)^6 + (sqrt2 -1)^6`


Show that 9n+1 – 8n – 9 is divisible by 64, whenever n is a positive integer.


Find a, b and n in the expansion of (a + b)n if the first three terms of the expansion are 729, 7290 and 30375, respectively.


Find a if the coefficients of x2 and x3 in the expansion of (3 + ax)9 are equal.


Evaluate `(sqrt3 + sqrt2)^6 - (sqrt3 - sqrt2)^6`


Expand using Binomial Theorem `(1+ x/2 - 2/x)^4, x != 0`


Evaluate: `(x^2 - sqrt(1 - x^2))^4 + (x^2 + sqrt(1 - x^2))^4`


Find the coefficient of x11 in the expansion of `(x^3 - 2/x^2)^12`


Determine whether the expansion of `(x^2 - 2/x)^18` will contain a term containing x10?


Which of the following is larger? 9950 + 10050  or 10150


The total number of terms in the expansion of (x + a)51 – (x – a)51 after simplification is ______.


If (1 – x + x2)n = a0 + a1 x + a2 x2 + ... + a2n x2n , then a0 + a2 + a4 + ... + a2n equals ______.


If z = `sqrt(3)/2 + i^5/2 + sqrt(3)/2 - i^5/2`, then ______.


Find the coefficient of x15 in the expansion of (x – x2)10.


Find the sixth term of the expansion `(y^(1/2) + x^(1/3))^"n"`, if the binomial coefficient of the third term from the end is 45.


If the coefficient of second, third and fourth terms in the expansion of (1 + x)2n are in A.P. Show that 2n2 – 9n + 7 = 0.


In the expansion of (x + a)n if the sum of odd terms is denoted by O and the sum of even term by E. Then prove that O2 – E2 = (x2 – a2)n 


Given the integers r > 1, n > 2, and coefficients of (3r)th and (r + 2)nd terms in the binomial expansion of (1 + x)2n are equal, then ______.


The number of terms in the expansion of (x + y + z)n ______.


The coefficient of a–6b4 in the expansion of `(1/a - (2b)/3)^10` is ______.


Number of terms in the expansion of (a + b)n where n ∈ N is one less than the power n.


Let the coefficients of x–1 and x–3 in the expansion of `(2x^(1/5) - 1/x^(1/5))^15`, x > 0, be m and n respectively. If r is a positive integer such that mn2 = 15Cr, 2r, then the value of r is equal to ______.


The sum of the last eight coefficients in the expansion of (1 + x)16 is equal to ______.


Let `(5 + 2sqrt(6))^n` = p + f where n∈N and p∈N and 0 < f < 1 then the value of f2 – f + pf – p is ______. 


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×