Advertisements
Advertisements
प्रश्न
Simplify the following products:
`(x^3 - 3x^2 - x)(x^2 - 3x + 1)`
Advertisements
उत्तर
We have,
`(x^3 - 3x^2 - x)(x^2 - 3x + 1)`
`=> x(x^2 - 3x - 1)(x^2 - 3x + 1)`
`=>x[[x^2 - 3x]^2 - [1]^2]` `[∵ (a - b)(a +b^2) = a^2 - b^2]`
`=> x[(x^2)^2 + (-3x)^2 - 2(+3x)x^2] - 1]`
`=> x[x^4 + 9x^2 - 6x^3 - 1]`
`=> x^5 - 6x^4 + 9x^3 - x`
`∴ (x^3 - 3x^2 - 2)(x^2 - 3x + 1) = x^5 - 6x^4 + 9x^3 - x`
APPEARS IN
संबंधित प्रश्न
Write the following cube in expanded form:
(2x + 1)3
Factorise the following:
8a3 + b3 + 12a2b + 6ab2
Verify that `x^3+y^3+z^3-3xyz=1/2(x+y+z)[(x-y)^2+(y-z)^2+(z-x)^2]`
Evaluate following using identities:
(a - 0.1) (a + 0.1)
Evaluate the following using identities:
117 x 83
Write in the expanded form (a2 + b2 + c2 )2
If \[x - \frac{1}{x} = - 1\] find the value of \[x^2 + \frac{1}{x^2}\]
If \[x - \frac{1}{x} = 5\], find the value of \[x^3 - \frac{1}{x^3}\]
Find the value of 27x3 + 8y3, if 3x + 2y = 14 and xy = 8
Find the value of 27x3 + 8y3, if 3x + 2y = 20 and xy = \[\frac{14}{9}\]
Find the following product:
(3x + 2y) (9x2 − 6xy + 4y2)
If x = 3 and y = − 1, find the values of the following using in identify:
\[\left( \frac{x}{7} + \frac{y}{3} \right) \left( \frac{x^2}{49} + \frac{y^2}{9} - \frac{xy}{21} \right)\]
If x + y + z = 8 and xy +yz +zx = 20, find the value of x3 + y3 + z3 −3xyz
If a + b + c = 9 and a2+ b2 + c2 =35, find the value of a3 + b3 + c3 −3abc
If \[x + \frac{1}{x} = 3\] then \[x^6 + \frac{1}{x^6}\] =
Evaluate `(a/[2b] + [2b]/a )^2 - ( a/[2b] - [2b]/a)^2 - 4`.
Use the direct method to evaluate the following products:
(a – 8) (a + 2)
Evaluate: `(4/7"a"+3/4"b")(4/7"a"-3/4"b")`
If a2 - 3a - 1 = 0 and a ≠ 0, find : `"a" + (1)/"a"`
Expand the following:
(3a – 2b)3
