Advertisements
Advertisements
प्रश्न
Find the following product:
(4x − 3y + 2z) (16x2 + 9y2 + 4z2 + 12xy + 6yz − 8zx)
Advertisements
उत्तर
In the given problem, we have to find Product of equations
Given (4x − 3y + 2z) (16x2 + 9y2 + 4z2 + 12xy + 6yz − 8zx)
We shall use the identity
`x^3 + y^3 + z^3 - 3xyz = (x+ y +z)(x^2 + y^2 + z^2 - xy - yz - zx)`
` = (4x)^3 + (3y)^3 + (2z)^3 -3 (4x)(3y)(2z)`
` = (4x) xx (4x) xx (4x) +(-3y) xx (-3y) xx (-3y) + (2z) xx (2z) xx (2z) -3 (4x) (-3y)(2z)`
` = 64x^3 - 27y^3 + 8z^3 + 72 xyz`
Hence the product of (4x − 3y + 2z) (16x2 + 9y2 + 4z2 + 12xy + 6yz − 8zx) is `64x^2 - 27y^3 + 8z^3 + 72xyz`
APPEARS IN
संबंधित प्रश्न
Expand the following, using suitable identity:
(x + 2y + 4z)2
Evaluate the following using suitable identity:
(998)3
If 9x2 + 25y2 = 181 and xy = −6, find the value of 3x + 5y
Simplify (2x + p - c)2 - (2x - p + c)2
Find the cube of the following binomials expression :
\[\frac{3}{x} - \frac{2}{x^2}\]
If 3x − 2y = 11 and xy = 12, find the value of 27x3 − 8y3
Evaluate of the following:
`(10.4)^3`
Find the value of 27x3 + 8y3, if 3x + 2y = 20 and xy = \[\frac{14}{9}\]
Find the following product:
Find the following product:
(3x + 2y + 2z) (9x2 + 4y2 + 4z2 − 6xy − 4yz − 6zx)
If x + y + z = 8 and xy +yz +zx = 20, find the value of x3 + y3 + z3 −3xyz
If a + b + c = 9 and a2+ b2 + c2 =35, find the value of a3 + b3 + c3 −3abc
If a − b = 5 and ab = 12, find the value of a2 + b2
Evalute : `( 7/8x + 4/5y)^2`
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.
If a2 - 5a - 1 = 0 and a ≠ 0 ; find:
- `a - 1/a`
- `a + 1/a`
- `a^2 - 1/a^2`
If x + y + z = p and xy + yz + zx = q; find x2 + y2 + z2.
Simplify:
(3a + 2b - c)(9a2 + 4b2 + c2 - 6ab + 2bc +3ca)
Expand the following:
(3a – 2b)3
