Advertisements
Advertisements
Question
(a − b)3 + (b − c)3 + (c − a)3 =
Options
(a + b + c) (a2 + b2 + c2 − ab − bc − ca)
(a − b) (b − c) (c − a)
3(a − b) ( b− c) (c − a)
none of these
Advertisements
Solution
Given `(a-b)^3 + (b-c)^3 + (c-a)^2`
Using identity `x^2 +y^3 +z^3 = 3xyz`
Here `x = a -b, y = b -c,z = c-a`
`(a-b)^3 +(b-c)^3 (c-a)^3 = 3(a-b )(b-c)(c-a)`
Hence the Value of `(a-b)^3+ (b-c)^3+(c-a)^3` is `3(a-b)(b-c)(c-a)`
APPEARS IN
RELATED QUESTIONS
Use suitable identity to find the following product:
(3 – 2x) (3 + 2x)
Evaluate the following using suitable identity:
(99)3
Evaluate the following using suitable identity:
(998)3
Evaluate the following using identities:
`(a^2b - b^2a)^2`
Simplify (2x + p - c)2 - (2x - p + c)2
If \[x - \frac{1}{x} = 7\], find the value of \[x^3 - \frac{1}{x^3}\].
Evaluate of the following:
(598)3
Evaluate of the following:
463+343
If \[x^4 + \frac{1}{x^4} = 119\] , find the value of \[x^3 - \frac{1}{x^3}\]
If a - b = 0.9 and ab = 0.36; find:
(i) a + b
(ii) a2 - b2.
The number x is 2 more than the number y. If the sum of the squares of x and y is 34, then find the product of x and y.
Evaluate: (4 − ab) (8 + ab)
Expand the following:
(3x + 4) (2x - 1)
Expand the following:
(x - 3y - 2z)2
Simplify by using formula :
(1 + a) (1 - a) (1 + a2)
If a2 - 3a - 1 = 0 and a ≠ 0, find : `"a" - (1)/"a"`
If a2 - 3a - 1 = 0 and a ≠ 0, find : `"a"^2 - (1)/"a"^2`
Expand the following:
(4a – b + 2c)2
Factorise the following:
9x2 + 4y2 + 16z2 + 12xy – 16yz – 24xz
If a + b + c = 9 and ab + bc + ca = 26, find a2 + b2 + c2.
