Advertisements
Advertisements
Question
Find the following product:
Solution
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
RELATED QUESTIONS
Factorise the following:
27y3 + 125z3
If x + y + z = 0, show that x3 + y3 + z3 = 3xyz.
If a + b + c = 0 and a2 + b2 + c2 = 16, find the value of ab + bc + ca.
Find the cube of the following binomials expression :
\[2x + \frac{3}{x}\]
Evaluate of the following:
(103)3
Evaluate of the following:
1043 + 963
Simplify of the following:
(x+3)3 + (x−3)3
If a + b = 6 and ab = 20, find the value of a3 − b3
Mark the correct alternative in each of the following:
If \[x + \frac{1}{x} = 5\] then \[x^2 + \frac{1}{x^2} = \]
If the volume of a cuboid is 3x2 − 27, then its possible dimensions are
If \[x - \frac{1}{x} = \frac{15}{4}\], then \[x + \frac{1}{x}\] =
Find the squares of the following:
`(7x)/(9y) - (9y)/(7x)`
Evaluate, using (a + b)(a - b)= a2 - b2.
399 x 401
If p + q = 8 and p - q = 4, find:
pq
If m - n = 0.9 and mn = 0.36, find:
m2 - n2.
If a2 - 3a - 1 = 0 and a ≠ 0, find : `"a" + (1)/"a"`
Simplify:
(4x + 5y)2 + (4x - 5y)2
Using suitable identity, evaluate the following:
1033
Find the following product:
(x2 – 1)(x4 + x2 + 1)
