Advertisements
Advertisements
Question
Find the following product:
Advertisements
Solution
Given `(2/x + 3x) (4/x^2 + 9x^2 - 6)`
We shall use the identity, `a^3+ b^3 = (a+b) (a^2 + b^2 - ab)`
We can rearrange the `(2/x + 3x) (4/x^3 + 9x^2 - 6)`as
`= (2/x + 3x)[(2/x)^2 + (3x)^2 - (2/x) (3x)]`
` = (2/x^3) + (3x)^3`
`= (2/x) xx (2/x) xx(2/x) + (3x) xx (3x) xx (3x)`
`= 8/x^3 + 27x^3`
Hence the Product value of `(2/x + 3x) (4/x^2 + 9x^2 - 6)`is `8/x^3 + 27x^3`.
APPEARS IN
RELATED QUESTIONS
Evaluate the following product without multiplying directly:
103 × 107
Simplify the following:
322 x 322 - 2 x 322 x 22 + 22 x 22
Simplify (a + b + c)2 + (a - b + c)2
Find the cube of the following binomials expression :
\[4 - \frac{1}{3x}\]
Find the following product:
If x = 3 and y = − 1, find the values of the following using in identify:
(9y2 − 4x2) (81y4 +36x2y2 + 16x4)
If x = 3 and y = − 1, find the values of the following using in identify:
\[\left( \frac{x}{7} + \frac{y}{3} \right) \left( \frac{x^2}{49} + \frac{y^2}{9} - \frac{xy}{21} \right)\]
Evaluate:
253 − 753 + 503
If \[x^3 + \frac{1}{x^3} = 110\], then \[x + \frac{1}{x} =\]
75 × 75 + 2 × 75 × 25 + 25 × 25 is equal to
If a2 - 3a + 1 = 0, and a ≠ 0; find:
- `a + 1/a`
- `a^2 + 1/a^2`
The difference between two positive numbers is 5 and the sum of their squares is 73. Find the product of these numbers.
Evaluate: (5xy − 7) (7xy + 9)
If a2 + b2 + c2 = 41 and a + b + c = 9; find ab + bc + ca.
If `"r" - (1)/"r" = 4`; find: `"r"^2 + (1)/"r"^2`
Find the following product:
`(x/2 + 2y)(x^2/4 - xy + 4y^2)`
Give possible expressions for the length and breadth of the rectangle whose area is given by 4a2 + 4a – 3.
If a + b + c = 5 and ab + bc + ca = 10, then prove that a3 + b3 + c3 – 3abc = – 25.
