Advertisements
Advertisements
प्रश्न
Find the following product:
Advertisements
उत्तर
Given `(x^2 - 1) (x^4+x^2 + 1)`
We shall use the identity `(a-b) (a^2 + ab + b^2) = a^3 - b^3`
We can rearrange the `(x^2 - 1)(x^4 + x^2 + 1)`as
\[\left( x^2 - 1 \right)\left[ \left( x^2 \right)^2 + \left( x^2 \right)\left( 1 \right) + \left( 1 \right)^2 \right]\]
`= (x^2)^3 - (1)^3`
` = (x^2) xx(x^2) xx (x^2) - (1) xx (1) xx (1)`
` = x^6 - 1^3`
` = x^6 - 1`
Hence the Product value of `(x^2 - 1) (x^4 +x^2 + 1)`is `x^6 - 1`.
APPEARS IN
संबंधित प्रश्न
Use suitable identity to find the following product:
(3 – 2x) (3 + 2x)
Write the following cube in expanded form:
(2x + 1)3
If `x + 1/x = sqrt5`, find the value of `x^2 + 1/x^2` and `x^4 + 1/x^4`
Simplify (a + b + c)2 + (a - b + c)2
If \[x + \frac{1}{x} = 3\] then \[x^6 + \frac{1}{x^6}\] =
If the volume of a cuboid is 3x2 − 27, then its possible dimensions are
The product (a + b) (a − b) (a2 − ab + b2) (a2 + ab + b2) is equal to
The difference between two positive numbers is 5 and the sum of their squares is 73. Find the product of these numbers.
Use the direct method to evaluate :
(ab+x2) (ab−x2)
Evaluate: (4 − ab) (8 + ab)
Evaluate: `(2"x"-3/5)(2"x"+3/5)`
Find the squares of the following:
9m - 2n
Simplify by using formula :
(a + b - c) (a - b + c)
If `"a" - 1/"a" = 10`; find `"a"^2 - 1/"a"^2`
If x + y = 1 and xy = -12; find:
x2 - y2.
If `"a"^2 - 7"a" + 1` = 0 and a = ≠ 0, find :
`"a"^2 + (1)/"a"^2`
If `"r" - (1)/"r" = 4`; find : `"r"^4 + (1)/"r"^4`
If `"a" + (1)/"a" = 2`, then show that `"a"^2 + (1)/"a"^2 = "a"^3 + (1)/"a"^3 = "a"^4 + (1)/"a"^4`
Simplify:
(1 + x)(1 - x)(1 - x + x2)(1 + x + x2)
If a + b + c = 0, then a3 + b3 + c3 is equal to ______.
