Advertisements
Advertisements
Question
Evaluate the following using suitable identity:
(998)3
Advertisements
Solution
It is known that,
(a + b)3 = a3 + b3 + 3ab(a + b) and (a − b)3 = a3 − b3 − 3ab(a − b)
∴ (998)3 = (1000 − 2)3
= (1000)3 − (2)3 − 3(1000)(2)(1000 − 2)
= 1000000000 − 8 − 6000(998)
= 1000000000 − 8 − 5988000
= 1000000000 − 5988008
= 994011992
APPEARS IN
RELATED QUESTIONS
Factorise the following:
`27p^3-1/216-9/2p^2+1/4p`
Without actually calculating the cubes, find the value of the following:
(–12)3 + (7)3 + (5)3
Write in the expanded form: (ab + bc + ca)2
Write in the expanded form:
`(a/(bc) + b/(ca) + c/(ab))^2`
If a − b = 4 and ab = 21, find the value of a3 −b3
Simplify of the following:
(x+3)3 + (x−3)3
Simplify of the following:
Find the following product:
(3x + 2y) (9x2 − 6xy + 4y2)
Find the following product:
(4x − 5y) (16x2 + 20xy + 25y2)
If x = 3 and y = − 1, find the values of the following using in identify:
\[\left( \frac{3}{x} - \frac{x}{3} \right) \left( \frac{x^2}{9} + \frac{9}{x^2} + 1 \right)\]
If a − b = −8 and ab = −12, then a3 − b3 =
(x − y) (x + y) (x2 + y2) (x4 + y4) is equal to ______.
Find the square of `(3a)/(2b) - (2b)/(3a)`.
Evalute : `((2x)/7 - (7y)/4)^2`
Evaluate : (4a +3b)2 - (4a - 3b)2 + 48ab.
Evaluate: (5xy − 7) (7xy + 9)
Find the squares of the following:
(2a + 3b - 4c)
Simplify:
(3a + 2b - c)(9a2 + 4b2 + c2 - 6ab + 2bc +3ca)
Simplify:
(3a - 7b + 3)(3a - 7b + 5)
Using suitable identity, evaluate the following:
9992
