Advertisements
Advertisements
Question
Find the following product:
(3x + 2y + 2z) (9x2 + 4y2 + 4z2 − 6xy − 4yz − 6zx)
Advertisements
Solution
In the given problem, we have to find Product of equations
Given (3x + 2y + 2z) (9x2 + 4y2 + 4z2 − 6xy − 4yz − 6zx)
We shall use the identity
`x^3 + y^3 + z^3 - 3xyz = (x+y+z) (x^2 + y^2 + z^2 - xy - yz - zx)`
` = (3x)^3 + (2y)^3 + (2z)^3 - 3 (3x)(2y)(2z)`
` =(3x) xx (3x) xx (3x) + (2y) xx(2y) xx(2y) + (2z) xx(2z) xx(2z)-3(3x)(2y)(2z) `
` = 27x^3 + 8y^3 + 8z^3 - 36xyz`
Hence the product of (3x + 2y + 2z) (9x2 + 4y2 + 4z2 − 6xy − 4yz − 6zx)is `27x^3 + 8y^3 + 8z^3 - 36xyz`
APPEARS IN
RELATED QUESTIONS
Expand the following, using suitable identity:
(2x – y + z)2
What are the possible expressions for the dimensions of the cuboids whose volume is given below?
| Volume : 12ky2 + 8ky – 20k |
Simplify the following products:
`(x/2 - 2/5)(2/5 - x/2) - x^2 + 2x`
Prove that a2 + b2 + c2 − ab − bc − ca is always non-negative for all values of a, b and c
Write in the expanded form:
`(2 + x - 2y)^2`
Simplify (a + b + c)2 + (a - b + c)2 + (a + b - c)2
If \[x - \frac{1}{x} = - 1\] find the value of \[x^2 + \frac{1}{x^2}\]
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
If x = 3 and y = − 1, find the values of the following using in identify:
\[\left( \frac{3}{x} - \frac{x}{3} \right) \left( \frac{x^2}{9} + \frac{9}{x^2} + 1 \right)\]
(a − b)3 + (b − c)3 + (c − a)3 =
(x − y) (x + y) (x2 + y2) (x4 + y4) is equal to ______.
If a + b = 7 and ab = 10; find a - b.
Simplify by using formula :
(x + y - 3) (x + y + 3)
Evaluate, using (a + b)(a - b)= a2 - b2.
399 x 401
Evaluate, using (a + b)(a - b)= a2 - b2.
15.9 x 16.1
The coefficient of x in the expansion of (x + 3)3 is ______.
Factorise the following:
9y2 – 66yz + 121z2
Find the following product:
(x2 – 1)(x4 + x2 + 1)
Without actually calculating the cubes, find the value of:
(0.2)3 – (0.3)3 + (0.1)3
