Advertisements
Advertisements
प्रश्न
Find the following product:
Advertisements
उत्तर
Given (x3 + 1) (x6 − x3 + 1)
We shall use the identity, `a^3 + b^3 = (a+ b) (a^2 + b^2 - ab)`
We can rearrange the `(x^3 + 1) (x^6 - x^3 + 1)`as
`= (x^3 + 1) [(x^3)^2 - (x^3)(1) + (1)^2]`
`= (x^3)^3 + (1)^3`
` = (x^3) xx (x^3)xx (x^3) + (1) xx (1) xx (1) `
` = x^9 + 1^3`
` = x^9 + 1`
Hence the Product value of `(x^3 + 1) (x^6 - x^3 + 1)`is .`x^9 + 1`.
APPEARS IN
संबंधित प्रश्न
Factorise the following:
64m3 – 343n3
Evaluate the following using identities:
(1.5x2 − 0.3y2) (1.5x2 + 0.3y2)
Simplify the following:
322 x 322 - 2 x 322 x 22 + 22 x 22
Simplify the following products:
`(x^3 - 3x^2 - x)(x^2 - 3x + 1)`
Write in the expanded form:
`(2 + x - 2y)^2`
Simplify (2x + p - c)2 - (2x - p + c)2
Simplify the following expressions:
`(x^2 - x + 1)^2 - (x^2 + x + 1)^2`
Evaluate of the following:
1113 − 893
Find the value of 64x3 − 125z3, if 4x − 5z = 16 and xz = 12.
Evaluate:
253 − 753 + 503
If \[x + \frac{1}{x} = 2\], then \[x^3 + \frac{1}{x^3} =\]
If \[x^3 - \frac{1}{x^3} = 14\],then \[x - \frac{1}{x} =\]
(a − b)3 + (b − c)3 + (c − a)3 =
If \[x^4 + \frac{1}{x^4} = 623\] then \[x + \frac{1}{x} =\]
Evaluate: 203 × 197
Expand the following:
(3x + 4) (2x - 1)
If x + y = 1 and xy = -12; find:
x - y
If `x + (1)/x = "p", x - (1)/x = "q"`; find the relation between p and q.
Simplify:
(2x - 4y + 7)(2x + 4y + 7)
Factorise the following:
25x2 + 16y2 + 4z2 – 40xy + 16yz – 20xz
