Advertisements
Advertisements
प्रश्न
Find the following product:
Advertisements
उत्तर
Given (x3 + 1) (x6 − x3 + 1)
We shall use the identity, `a^3 + b^3 = (a+ b) (a^2 + b^2 - ab)`
We can rearrange the `(x^3 + 1) (x^6 - x^3 + 1)`as
`= (x^3 + 1) [(x^3)^2 - (x^3)(1) + (1)^2]`
`= (x^3)^3 + (1)^3`
` = (x^3) xx (x^3)xx (x^3) + (1) xx (1) xx (1) `
` = x^9 + 1^3`
` = x^9 + 1`
Hence the Product value of `(x^3 + 1) (x^6 - x^3 + 1)`is .`x^9 + 1`.
APPEARS IN
संबंधित प्रश्न
Use suitable identity to find the following product:
`(y^2+3/2)(y^2-3/2)`
Evaluate the following using identities:
(1.5x2 − 0.3y2) (1.5x2 + 0.3y2)
Evaluate following using identities:
991 ☓ 1009
If a2 + b2 + c2 = 16 and ab + bc + ca = 10, find the value of a + b + c.
Find the value of 27x3 + 8y3, if 3x + 2y = 20 and xy = \[\frac{14}{9}\]
If a + b + c = 9 and a2+ b2 + c2 =35, find the value of a3 + b3 + c3 −3abc
If \[x + \frac{1}{x}\] 4, then \[x^4 + \frac{1}{x^4} =\]
If \[x^3 + \frac{1}{x^3} = 110\], then \[x + \frac{1}{x} =\]
The product (x2−1) (x4 + x2 + 1) is equal to
Use the direct method to evaluate the following products :
(y + 5)(y – 3)
Use the direct method to evaluate the following products :
(8 – b) (3 + b)
Use the direct method to evaluate :
(x+1) (x−1)
Use the direct method to evaluate :
(xy+4) (xy−4)
Find the squares of the following:
`(7x)/(9y) - (9y)/(7x)`
Evaluate the following :
1.81 x 1.81 - 1.81 x 2.19 + 2.19 x 2.19
The value of 2492 – 2482 is ______.
Find the following product:
`(x/2 + 2y)(x^2/4 - xy + 4y^2)`
If a + b + c = 5 and ab + bc + ca = 10, then prove that a3 + b3 + c3 – 3abc = – 25.
Prove that (a + b + c)3 – a3 – b3 – c3 = 3(a + b)(b + c)(c + a).
