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
Factorise:
4x2 + 9y2 + 16z2 + 12xy – 24yz – 16xz
Write in the expanded form: (-2x + 3y + 2z)2
Simplify (a + b + c)2 + (a - b + c)2 + (a + b - c)2
Find the cube of the following binomials expression :
\[\frac{3}{x} - \frac{2}{x^2}\]
Evaluate of the following:
1113 − 893
Find the following product:
Find the following product:
If x = 3 and y = − 1, find the values of the following using in identify:
\[\left( \frac{5}{x} + 5x \right)\] \[\left( \frac{25}{x^2} - 25 + 25 x^2 \right)\]
If \[x + \frac{1}{x} = 3\] then find the value of \[x^6 + \frac{1}{x^6}\].
If \[x - \frac{1}{x} = \frac{1}{2}\],then write the value of \[4 x^2 + \frac{4}{x^2}\]
If a + b + c = 9 and ab + bc + ca = 23, then a2 + b2 + c2 =
The product (a + b) (a − b) (a2 − ab + b2) (a2 + ab + b2) is equal to
Evalute : `((2x)/7 - (7y)/4)^2`
Use the direct method to evaluate :
`("a"/2-"b"/3)("a"/2+"b"/3)`
Evaluate: `(3"x"+1/2)(2"x"+1/3)`
Expand the following:
(2x - 5) (2x + 5) (2x- 3)
If 2x + 3y = 10 and xy = 5; find the value of 4x2 + 9y2
Simplify:
(x + 2y + 3z)(x2 + 4y2 + 9z2 - 2xy - 6yz - 3zx)
Expand the following:
(3a – 2b)3
