Advertisements
Advertisements
Question
Evaluate following using identities:
991 ☓ 1009
Advertisements
Solution
In the given problem, we have to evaluate expressions by using identities.
The given expression is 991 x 1009
We have `(991 + 1009)/2 = 1000`
So we can express 991 and 1009 in the terms of 1000 as
991 = 1000 - 9
1009 = 1000 + 9
`991 xx 1009 = (1000 - 9)(1000 + 9)`
We shall use the identity `(x - y)(x + y) = x^2 - y^2`
Here
(x - y) = (1000 - 9)
(x + y) = (1000 + 9)
By applying in identity we get
`(1000 - 9)(1000 + 9) = (1000)^2 - (9)^2`
= 1000000 - 81
= 999919
Hence the value of 991 x 1009 is 999919
APPEARS IN
RELATED QUESTIONS
Factorise:
`2x^2 + y^2 + 8z^2 - 2sqrt2xy + 4sqrt2yz - 8xz`
Factorise the following:
27y3 + 125z3
If 3x - 7y = 10 and xy = -1, find the value of `9x^2 + 49y^2`
If a − b = 4 and ab = 21, find the value of a3 −b3
Evaluate of the following:
1043 + 963
Find the value of 27x3 + 8y3, if 3x + 2y = 20 and xy = \[\frac{14}{9}\]
If x = 3 and y = − 1, find the values of the following using in identify:
\[\left( \frac{5}{x} + 5x \right)\] \[\left( \frac{25}{x^2} - 25 + 25 x^2 \right)\]
If a + b = 8 and ab = 6, find the value of a3 + b3
If \[\frac{a}{b} + \frac{b}{a} = - 1\] then a3 − b3 =
If the volume of a cuboid is 3x2 − 27, then its possible dimensions are
If \[3x + \frac{2}{x} = 7\] , then \[\left( 9 x^2 - \frac{4}{x^2} \right) =\]
\[\frac{( a^2 - b^2 )^3 + ( b^2 - c^2 )^3 + ( c^2 - a^2 )^3}{(a - b )^3 + (b - c )^3 + (c - a )^3} =\]
Find the square of : 3a - 4b
Find the square of `(3a)/(2b) - (2b)/(3a)`.
Use the direct method to evaluate the following products :
(b – 3) (b – 5)
Use the direct method to evaluate :
`("z"-2/3)("z"+2/3)`
If `"a" + 1/"a" = 6;`find `"a"^2 - 1/"a"^2`
If a + b + c = 0, then a3 + b3 + c3 is equal to ______.
If a + b + c = 5 and ab + bc + ca = 10, then prove that a3 + b3 + c3 – 3abc = – 25.
