Advertisements
Advertisements
प्रश्न
Find the following product:
(2ab − 3b − 2c) (4a2 + 9b2 +4c2 + 6 ab − 6 bc + 4ca)
Advertisements
उत्तर
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
संबंधित प्रश्न
Expand the following, using suitable identity:
(–2x + 3y + 2z)2
Evaluate the following using identities:
(2x + y) (2x − y)
Simplify the following: 175 x 175 x 2 x 175 x 25 x 25 x 25
If 2x + 3y = 8 and xy = 2 find the value of `4x^2 + 9y^2`
Simplify the following product:
(x2 + x − 2)(x2 − x + 2)
Simplify `(x^2 + y^2 - z)^2 - (x^2 - y^2 + z^2)^2`
Find the cube of the following binomials expression :
\[\frac{1}{x} + \frac{y}{3}\]
Find the cube of the following binomials expression :
\[2x + \frac{3}{x}\]
If \[x + \frac{1}{x} = 5\], find the value of \[x^3 + \frac{1}{x^3}\]
If x = 3 and y = − 1, find the values of the following using in identify:
\[\left( \frac{x}{7} + \frac{y}{3} \right) \left( \frac{x^2}{49} + \frac{y^2}{9} - \frac{xy}{21} \right)\]
(a − b)3 + (b − c)3 + (c − a)3 =
Use the direct method to evaluate :
(0.5−2a) (0.5+2a)
Find the squares of the following:
3p - 4q2
Find the squares of the following:
(2a + 3b - 4c)
Evaluate, using (a + b)(a - b)= a2 - b2.
999 x 1001
If p2 + q2 + r2 = 82 and pq + qr + pr = 18; find p + q + r.
Simplify:
`("a" - 1/"a")^2 + ("a" + 1/"a")^2`
Using suitable identity, evaluate the following:
101 × 102
Find the following product:
`(x/2 + 2y)(x^2/4 - xy + 4y^2)`
Without actually calculating the cubes, find the value of:
`(1/2)^3 + (1/3)^3 - (5/6)^3`
