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
Give possible expression for the length and breadth of the following rectangle, in which their area are given:
| Area : 25a2 – 35a + 12 |
Evaluate the following using identities:
(399)2
Write the expanded form:
`(-3x + y + z)^2`
Find the value of 64x3 − 125z3, if 4x − 5z = 16 and xz = 12.
Find the following product:
(3x + 2y + 2z) (9x2 + 4y2 + 4z2 − 6xy − 4yz − 6zx)
If \[x^3 + \frac{1}{x^3} = 110\], then \[x + \frac{1}{x} =\]
If \[\frac{a}{b} + \frac{b}{a} = - 1\] then a3 − b3 =
If \[x^4 + \frac{1}{x^4} = 623\] then \[x + \frac{1}{x} =\]
If 49a2 − b = \[\left( 7a + \frac{1}{2} \right) \left( 7a - \frac{1}{2} \right)\] then the value of b is
Find the square of : 3a - 4b
If a - b = 0.9 and ab = 0.36; find:
(i) a + b
(ii) a2 - b2.
Evaluate: `(4/7"a"+3/4"b")(4/7"a"-3/4"b")`
Expand the following:
(a + 4) (a + 7)
Simplify by using formula :
(x + y - 3) (x + y + 3)
Simplify by using formula :
(1 + a) (1 - a) (1 + a2)
Simplify by using formula :
`("a" + 2/"a" - 1) ("a" - 2/"a" - 1)`
If m - n = 0.9 and mn = 0.36, find:
m + n
Using suitable identity, evaluate the following:
101 × 102
Factorise the following:
`(2x + 1/3)^2 - (x - 1/2)^2`
