Advertisements
Advertisements
Question
Evaluate the following using suitable identity:
(99)3
Advertisements
Solution
It is known that,
(a + b)3 = a3 + b3 + 3ab(a + b) and (a − b)3 = a3 − b3 − 3ab(a − b)
∴ (99)3 = (100 − 1)3
= (100)3 − (1)3 − 3(100)(1)(100 − 1)
= 1000000 − 1 − 300(99)
= 1000000 − 1 − 29700
= 970299
APPEARS IN
RELATED QUESTIONS
Evaluate the following product without multiplying directly:
95 × 96
Evaluate the following using suitable identity:
(102)3
Give possible expression for the length and breadth of the following rectangle, in which their area is given:
| Area : 35y2 + 13y – 12 |
if `x + 1/x = 11`, find the value of `x^2 + 1/x^2`
If `x^2 + 1/x^2 = 66`, find the value of `x - 1/x`
Find the cube of the following binomials expression :
\[2x + \frac{3}{x}\]
Find the following product:
\[\left( \frac{x}{2} + 2y \right) \left( \frac{x^2}{4} - xy + 4 y^2 \right)\]
If \[x + \frac{1}{x} = 3\] then find the value of \[x^6 + \frac{1}{x^6}\].
If the volume of a cuboid is 3x2 − 27, then its possible dimensions are
If \[3x + \frac{2}{x} = 7\] , then \[\left( 9 x^2 - \frac{4}{x^2} \right) =\]
If a + b + c = 9 and ab + bc + ca =23, then a3 + b3 + c3 − 3abc =
If 3x + 4y = 16 and xy = 4, find the value of 9x2 + 16y2.
Use the direct method to evaluate :
(3x2+5y2) (3x2−5y2)
Evaluate: (5xy − 7) (7xy + 9)
If x + y = 9, xy = 20
find: x2 - y2.
Simplify:
(3a - 7b + 3)(3a - 7b + 5)
Which one of the following is a polynomial?
If `49x^2 - b = (7x + 1/2)(7x - 1/2)`, then the value of b is ______.
Factorise the following:
16x2 + 4y2 + 9z2 – 16xy – 12yz + 24xz
Expand the following:
`(1/x + y/3)^3`
