Advertisements
Advertisements
Question
Evaluate of the following:
1113 − 893
Solution
In the given problem, we have to find the value of numbers
Given 1113 − 893
We can write 1113 − 893 as `(100+ 11)^3 - (100 - 11)^3`
We shall use the identity `(a+b)^3 - (a-b)^3 = 2[b^3 + 3a^2b]`
Here a=100 , b = 11
\[{111}^3 - {89}^3 = \left( 100 + 11 \right)^3 - \left( 100 - 11 \right)^3\]
`= 2[11^3 + 3 (100)^2(11)]`
`= 2 [1331 + 330000]`
`= 2 [331331]`
` = 662662`
Hence the value of 1113 − 893 is 662662 .
APPEARS IN
RELATED QUESTIONS
Factorise:
4x2 + 9y2 + 16z2 + 12xy – 24yz – 16xz
Factorise the following:
64a3 – 27b3 – 144a2b + 108ab2
Factorise the following:
`27p^3-1/216-9/2p^2+1/4p`
Factorise:
27x3 + y3 + z3 – 9xyz
Evaluate following using identities:
(a - 0.1) (a + 0.1)
Find the cube of the following binomials expression :
\[\frac{1}{x} + \frac{y}{3}\]
If a + b + c = 0, then write the value of \[\frac{a^2}{bc} + \frac{b^2}{ca} + \frac{c^2}{ab}\]
If a2 + b2 + c2 − ab − bc − ca =0, then
If a + b + c = 0, then \[\frac{a^2}{bc} + \frac{b^2}{ca} + \frac{c^2}{ab} =\]
If a + b = 7 and ab = 10; find a - b.
Use the direct method to evaluate :
`("a"/2-"b"/3)("a"/2+"b"/3)`
Evaluate: `(3"x"+1/2)(2"x"+1/3)`
Evaluate: (2a + 0.5) (7a − 0.3)
Evaluate: `(4/7"a"+3/4"b")(4/7"a"-3/4"b")`
Evaluate: `(2"a"+1/"2a")(2"a"-1/"2a")`
Evaluate, using (a + b)(a - b)= a2 - b2.
399 x 401
If `"a" + 1/"a" = 6;`find `"a" - 1/"a"`
If `"r" - (1)/"r" = 4`; find: `"r"^2 + (1)/"r"^2`
Expand the following:
(3a – 5b – c)2
Find the following product:
(x2 – 1)(x4 + x2 + 1)
