Advertisements
Advertisements
प्रश्न
Find the following product:
(3x + 2y + 2z) (9x2 + 4y2 + 4z2 − 6xy − 4yz − 6zx)
Advertisements
उत्तर
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
संबंधित प्रश्न
Evaluate the following product without multiplying directly:
95 × 96
Factorise the following using appropriate identity:
4y2 – 4y + 1
Factorise the following:
8a3 + b3 + 12a2b + 6ab2
Evaluate the following using identities:
(399)2
Simplify the following products:
`(m + n/7)^3 (m - n/7)`
Prove that a2 + b2 + c2 − ab − bc − ca is always non-negative for all values of a, b and c
If x = 3 and y = − 1, find the values of the following using in identify:
\[\left( \frac{x}{7} + \frac{y}{3} \right) \left( \frac{x^2}{49} + \frac{y^2}{9} - \frac{xy}{21} \right)\]
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 \[x^3 + \frac{1}{x^3} =\]
If \[x + \frac{1}{x} = 3\] then \[x^6 + \frac{1}{x^6}\] =
The product (x2−1) (x4 + x2 + 1) is equal to
Find the square of : 3a - 4b
If a + b = 7 and ab = 10; find a - b.
Find the squares of the following:
9m - 2n
Simplify by using formula :
(1 + a) (1 - a) (1 + a2)
Evaluate, using (a + b)(a - b)= a2 - b2.
4.9 x 5.1
If p2 + q2 + r2 = 82 and pq + qr + pr = 18; find p + q + r.
Using suitable identity, evaluate the following:
9992
Factorise the following:
`(2x + 1/3)^2 - (x - 1/2)^2`
