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
Expand the following, using suitable identity:
(–2x + 5y – 3z)2
Evaluate the following using identities:
(2x + y) (2x − y)
Find the cube of the following binomials expression :
\[\frac{1}{x} + \frac{y}{3}\]
Evaluate of the following:
1043 + 963
Find the following product:
If x = −2 and y = 1, by using an identity find the value of the following
Use the direct method to evaluate the following products :
(8 – b) (3 + b)
Use the direct method to evaluate :
`("z"-2/3)("z"+2/3)`
Evaluate: `(2"a"+1/"2a")(2"a"-1/"2a")`
Expand the following:
(x - 5) (x - 4)
Expand the following:
(2x - 5) (2x + 5) (2x- 3)
Evaluate the following without multiplying:
(95)2
If a - b = 10 and ab = 11; find a + b.
If p2 + q2 + r2 = 82 and pq + qr + pr = 18; find p + q + r.
Simplify:
`(x - 1/x)(x^2 + 1 + 1/x^2)`
Simplify:
(3x + 5y + 2z)(3x - 5y + 2z)
Without actually calculating the cubes, find the value of:
`(1/2)^3 + (1/3)^3 - (5/6)^3`
Without actually calculating the cubes, find the value of:
(0.2)3 – (0.3)3 + (0.1)3
Find the value of x3 + y3 – 12xy + 64, when x + y = – 4
