Advertisements
Advertisements
Question
Evaluate of the following:
1113 − 893
Advertisements
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
Expand the following, using suitable identity:
(3a – 7b – c)2
Factorise the following:
8a3 + b3 + 12a2b + 6ab2
Without actually calculating the cubes, find the value of the following:
(–12)3 + (7)3 + (5)3
Evaluate the following using identities:
`(2x+ 1/x)^2`
Simplify the following products:
`(m + n/7)^3 (m - n/7)`
Write in the expanded form:
`(a + 2b + c)^2`
Evaluate of the following:
(99)3
Find the following product:
\[\left( \frac{x}{2} + 2y \right) \left( \frac{x^2}{4} - xy + 4 y^2 \right)\]
Find the following product:
Evaluate:
483 − 303 − 183
If x + y + z = 8 and xy +yz +zx = 20, find the value of x3 + y3 + z3 −3xyz
Use identities to evaluate : (97)2
Evaluate: `(3"x"+1/2)(2"x"+1/3)`
Expand the following:
(3x + 4) (2x - 1)
Expand the following:
`(2"a" + 1/(2"a"))^2`
If `"a"^2 - 7"a" + 1` = 0 and a = ≠ 0, find :
`"a" + (1)/"a"`
If a2 - 3a - 1 = 0 and a ≠ 0, find : `"a" - (1)/"a"`
Which one of the following is a polynomial?
Expand the following:
(4a – b + 2c)2
Find the value of x3 + y3 – 12xy + 64, when x + y = – 4
