Advertisements
Advertisements
Question
Find the following product:
Advertisements
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
Use suitable identity to find the following product:
(3 – 2x) (3 + 2x)
Write the following cube in expanded form:
(2a – 3b)3
Simplify the following:
322 x 322 - 2 x 322 x 22 + 22 x 22
Write in the expanded form: `(x/y + y/z + z/x)^2`
Write in the expand form: `(2x - y + z)^2`
If a − b = 4 and ab = 21, find the value of a3 −b3
Simplify of the following:
Find the following product:
Find the square of : 3a + 7b
Find the square of : 3a - 4b
Evaluate `(a/[2b] + [2b]/a )^2 - ( a/[2b] - [2b]/a)^2 - 4`.
The number x is 2 more than the number y. If the sum of the squares of x and y is 34, then find the product of x and y.
Evaluate: `(3"x"+1/2)(2"x"+1/3)`
Evaluate: 203 × 197
If `x + (1)/x = 3`; find `x^4 + (1)/x^4`
Simplify:
(1 + x)(1 - x)(1 - x + x2)(1 + x + x2)
The value of 2492 – 2482 is ______.
Expand the following:
(–x + 2y – 3z)2
Expand the following:
(3a – 2b)3
Multiply x2 + 4y2 + z2 + 2xy + xz – 2yz by (–z + x – 2y).
