Advertisements
Advertisements
Question
Find the following product:
(2ab − 3b − 2c) (4a2 + 9b2 +4c2 + 6 ab − 6 bc + 4ca)
Advertisements
Solution
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
RELATED QUESTIONS
Use suitable identity to find the following product:
(x + 4) (x + 10)
Use suitable identity to find the following product:
`(y^2+3/2)(y^2-3/2)`
Expand the following, using suitable identity:
`[1/4a-1/2b+1]^2`
Write the following cube in expanded form:
(2a – 3b)3
Verify:
x3 – y3 = (x – y) (x2 + xy + y2)
Verify that `x^3+y^3+z^3-3xyz=1/2(x+y+z)[(x-y)^2+(y-z)^2+(z-x)^2]`
Simplify the following: 175 x 175 x 2 x 175 x 25 x 25 x 25
If `x + 1/x = sqrt5`, find the value of `x^2 + 1/x^2` and `x^4 + 1/x^4`
Write in the expanded form:
`(m + 2n - 5p)^2`
If \[x - \frac{1}{x} = - 1\] find the value of \[x^2 + \frac{1}{x^2}\]
If a − b = 4 and ab = 21, find the value of a3 −b3
Evaluate:
483 − 303 − 183
If x + y + z = 8 and xy +yz +zx = 20, find the value of x3 + y3 + z3 −3xyz
If \[x + \frac{1}{x} = 2\], then \[x^3 + \frac{1}{x^3} =\]
Use the direct method to evaluate the following products:
(x + 8)(x + 3)
Use the direct method to evaluate the following products :
(3x – 2y) (2x + y)
If x + y = 9, xy = 20
find: x2 - y2.
If a2 - 3a - 1 = 0 and a ≠ 0, find : `"a" - (1)/"a"`
If `"r" - (1)/"r" = 4`; find: `"r"^2 + (1)/"r"^2`
Find the value of x3 – 8y3 – 36xy – 216, when x = 2y + 6
