Advertisements
Advertisements
प्रश्न
Find the following product:
(2ab − 3b − 2c) (4a2 + 9b2 +4c2 + 6 ab − 6 bc + 4ca)
Advertisements
उत्तर
In the given problem, we have to find Product of equations
Given `(2a - 3b - 2c)(4a^2 + 9b^2 + 4c^2 + 6ab - 6bc +8ca)`
We shall use the identity
`x^3 + y^3 + z^3 - 3xyz = (x+y+ z) (x^2 + y^2 + z^2 - xy - yz - zx)`
` = (2a)^3 + (3b)^3 + (2c)^3 - 3 (2a )(3b)(2c)`
` = (2a) xx(2a) xx(2a) +(-3b) xx (-3b) xx(-3b)+ ( -2c) xx ( -2c) xx ( -2c) -3 (2a)(-3b)(-2c)`
` = 8a^3 - 27b^3 - 8c^3 - 36abc`
Hence the product of `(2a - 3b - 2c)(4a^2 + 9b^2 + 4c^2 + 6ab - 6bc +8ca)` is `8a^3 - 27b^3 - 8c^3 - 36abc`.
APPEARS IN
संबंधित प्रश्न
Use suitable identity to find the following product:
(x + 4) (x + 10)
Evaluate the following using suitable identity:
(99)3
Factorise the following:
8a3 + b3 + 12a2b + 6ab2
Simplify the following:
322 x 322 - 2 x 322 x 22 + 22 x 22
Write in the expanded form (a2 + b2 + c2 )2
Write in the expanded form:
`(a/(bc) + b/(ca) + c/(ab))^2`
Find the value of 64x3 − 125z3, if 4x − 5z = 16 and xz = 12.
If `x - 1/x = 3 + 2sqrt2`, find the value of `x^3 - 1/x^3`
Find the following product:
If a + b = 10 and ab = 16, find the value of a2 − ab + b2 and a2 + ab + b2
Evaluate:
253 − 753 + 503
If \[x^4 + \frac{1}{x^4} = 194,\] then \[x^3 + \frac{1}{x^3} =\]
If \[3x + \frac{2}{x} = 7\] , then \[\left( 9 x^2 - \frac{4}{x^2} \right) =\]
Expand the following:
(a + 4) (a + 7)
Simplify by using formula :
(1 + a) (1 - a) (1 + a2)
If x + y = 9, xy = 20
find: x2 - y2.
Simplify:
(4x + 5y)2 + (4x - 5y)2
Evaluate the following :
1.81 x 1.81 - 1.81 x 2.19 + 2.19 x 2.19
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
