Advertisements
Advertisements
Question
Find the following product:
Advertisements
Solution
Given `(1-x)(1 + x + x^2)`
We shall use the identity `(a-b)(a^2+ ab + b^2) = a^3 - b^3`
We can rearrange the `(1 - x) (1+ x + x^2)`as
` = (1- x) [(1)^2 + (1)(x)+ (x)^2]`
` = (1)^3 - (x)^3`
` = (1) xx (1) xx (1) - (x) xx (x) xx (x)`
` = 1=x^3`
Hence the Product value of `(1-x)(1+x + x^2)`is `1-x^3`.
APPEARS IN
RELATED QUESTIONS
Factorise the following using appropriate identity:
4y2 – 4y + 1
Expand the following, using suitable identity:
(3a – 7b – c)2
Evaluate following using identities:
(a - 0.1) (a + 0.1)
if `x + 1/x = 11`, find the value of `x^2 + 1/x^2`
Simplify (a + b + c)2 + (a - b + c)2 + (a + b - c)2
Simplify (2x + p - c)2 - (2x - p + 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 :
\[2x + \frac{3}{x}\]
Find the value of 27x3 + 8y3, if 3x + 2y = 20 and xy = \[\frac{14}{9}\]
The product (x2−1) (x4 + x2 + 1) is equal to
If a - b = 4 and a + b = 6; find
(i) a2 + b2
(ii) ab
If a2 - 3a + 1 = 0, and a ≠ 0; find:
- `a + 1/a`
- `a^2 + 1/a^2`
If `x + (1)/x = 3`; find `x^4 + (1)/x^4`
If m - n = 0.9 and mn = 0.36, find:
m2 - n2.
If 2x + 3y = 10 and xy = 5; find the value of 4x2 + 9y2
Simplify:
(1 + x)(1 - x)(1 - x + x2)(1 + x + x2)
Evaluate the following :
1.81 x 1.81 - 1.81 x 2.19 + 2.19 x 2.19
The coefficient of x in the expansion of (x + 3)3 is ______.
Factorise the following:
9y2 – 66yz + 121z2
Factorise the following:
`(2x + 1/3)^2 - (x - 1/2)^2`
