Advertisements
Advertisements
प्रश्न
Find the cube of the following binomials expression :
\[\frac{3}{x} - \frac{2}{x^2}\]
Advertisements
उत्तर
Given `(3/x-2/x^2)^3`
We shall use the identity `(a-b^3 ) = a^3-b^3- 3ab(a-b)`
Here `a=3/x,b = 2/x^2`
By applying the identity we get
`(3/x-2/x^2)^3 = (3/x)^3 - (2/x^2)^3 -3 (3/x)(2/x^2)(3/x-2/x^2)`
`= 27/x^3 - 8/x^6 -3 xx3/x xx 2/x^2 (3/x - 2/x^2)`
`= 27/x^3 - 8/x^6 -18/x^3(3/x - 2/x^2)`
`= 27/x^3 - 8/x^6 -(18/x^3 xx3/x) -(18/x^3xx2/x^2)`
`= 27/x^3 - 8/x^6 -(54/x^4 +36/x^5)`
`= 27/x^3 - 8/x^6 -54/x^4 +36/x^5`
Hence cube of the binomial expression of `(3/x-2/x^2)` is `= 27/x^3 - 8/x^6 -54/x^4 +36/x^5`.
APPEARS IN
संबंधित प्रश्न
Evaluate the following product without multiplying directly:
95 × 96
Factorise:
4x2 + 9y2 + 16z2 + 12xy – 24yz – 16xz
Write the following cube in expanded form:
`[x-2/3y]^3`
Give possible expression for the length and breadth of the following rectangle, in which their area are given:
| Area : 25a2 – 35a + 12 |
Evaluate following using identities:
(a - 0.1) (a + 0.1)
Simplify the following:
0.76 x 0.76 - 2 x 0.76 x 0.24 x 0.24 + 0.24
Evaluate the following:
(98)3
Evaluate of the following:
(9.9)3
If `x - 1/x = 3 + 2sqrt2`, find the value of `x^3 - 1/x^3`
If \[x^3 - \frac{1}{x^3} = 14\],then \[x - \frac{1}{x} =\]
(a − b)3 + (b − c)3 + (c − a)3 =
If \[\frac{a}{b} + \frac{b}{a} = - 1\] then a3 − b3 =
If \[3x + \frac{2}{x} = 7\] , then \[\left( 9 x^2 - \frac{4}{x^2} \right) =\]
If 49a2 − b = \[\left( 7a + \frac{1}{2} \right) \left( 7a - \frac{1}{2} \right)\] then the value of b is
Use the direct method to evaluate :
(2a+3) (2a−3)
Evaluate: `(3"x"+1/2)(2"x"+1/3)`
Expand the following:
(m + 8) (m - 7)
Expand the following:
(x - 5) (x - 4)
If x + y = 9, xy = 20
find: x - y
Find the value of x3 – 8y3 – 36xy – 216, when x = 2y + 6
