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
Write the following cube in expanded form:
(2x + 1)3
Evaluate the following using suitable identity:
(102)3
Simplify the following:
322 x 322 - 2 x 322 x 22 + 22 x 22
Write in the expanded form:
`(a/(bc) + b/(ca) + c/(ab))^2`
Find the value of 4x2 + y2 + 25z2 + 4xy − 10yz − 20zx when x = 4, y = 3 and z = 2.
Evaluate of the following:
463+343
Find the following product:
(7p4 + q) (49p8 − 7p4q + q2)
If x + y + z = 8 and xy +yz +zx = 20, find the value of x3 + y3 + z3 −3xyz
If a − b = 5 and ab = 12, find the value of a2 + b2
The number x is 2 more than the number y. If the sum of the squares of x and y is 34, then find the product of x and y.
Use the direct method to evaluate :
(2+a) (2−a)
Use the direct method to evaluate :
(2a+3) (2a−3)
Use the direct method to evaluate :
(0.5−2a) (0.5+2a)
Simplify by using formula :
(2x + 3y) (2x - 3y)
Evaluate the following without multiplying:
(999)2
If `"a" - 1/"a" = 10`; find `"a"^2 - 1/"a"^2`
If a2 - 3a - 1 = 0 and a ≠ 0, find : `"a" + (1)/"a"`
Factorise the following:
9x2 + 4y2 + 16z2 + 12xy – 16yz – 24xz
Give possible expressions for the length and breadth of the rectangle whose area is given by 4a2 + 4a – 3.
