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
Use suitable identity to find the following product:
(3x + 4) (3x – 5)
Evaluate the following product without multiplying directly:
104 × 96
Give possible expression for the length and breadth of the following rectangle, in which their area is given:
| Area : 35y2 + 13y – 12 |
if `x + 1/x = 11`, find the value of `x^2 + 1/x^2`
Simplify the following products:
`(m + n/7)^3 (m - n/7)`
Simplify the following products:
`(2x^4 - 4x^2 + 1)(2x^4 - 4x^2 - 1)`
Find the cube of the following binomials expression :
\[\frac{3}{x} - \frac{2}{x^2}\]
If \[x^2 + \frac{1}{x^2} = 98\] ,find the value of \[x^3 + \frac{1}{x^3}\]
Evaluate of the following:
(598)3
Find the following product:
\[\left( \frac{3}{x} - \frac{5}{y} \right) \left( \frac{9}{x^2} + \frac{25}{y^2} + \frac{15}{xy} \right)\]
If x = 3 and y = − 1, find the values of the following using in identify:
\[\left( \frac{x}{y} - \frac{y}{3} \right) \frac{x^2}{16} + \frac{xy}{12} + \frac{y^2}{9}\]
The product (a + b) (a − b) (a2 − ab + b2) (a2 + ab + b2) is equal to
If 49a2 − b = \[\left( 7a + \frac{1}{2} \right) \left( 7a - \frac{1}{2} \right)\] then the value of b is
If a - `1/a`= 8 and a ≠ 0 find :
(i) `a + 1/a (ii) a^2 - 1/a^2`
Use the direct method to evaluate :
(2+a) (2−a)
Use the direct method to evaluate :
(ab+x2) (ab−x2)
If `x + (1)/x = 3`; find `x^4 + (1)/x^4`
If `"a"^2 + (1)/"a"^2 = 14`; find the value of `"a" + (1)/"a"`
If `"a" + (1)/"a" = 2`, then show that `"a"^2 + (1)/"a"^2 = "a"^3 + (1)/"a"^3 = "a"^4 + (1)/"a"^4`
