Advertisements
Advertisements
Question
Factorize the following expressions:
`a^3 - 1/a^3 - 2a + 2/a`
Advertisements
Solution
`= (a^3 - 1/a^3) - 2(a - 1/a)`
`= (a^3 - (1/a)^3) - 2(a - 1/a)`
`= (a - 1/a)(a^2 + a xx 1/a + (1/a)^2) - 2(a - 1/a)` `[∵ a^3 - b^3 = (a - b)(a^2 + ab + b^2)]`
`= (a - 1/a)(a^2 + 1 + 1/a^2) - 2(a - 1/a)`
`= (a - 1/a)(a^2 + 1 + 1/a^2 - 2)`
`=(a - 1/a)(a^2 + 1 + -1)`
`∴ a^3 - 1/a^3 - 2a + 2/a = (a- 1/a)(a^2 + 1/a^2 - 1)`
APPEARS IN
RELATED QUESTIONS
Get the algebraic expression in the following case using variables, constants and arithmetic operations.
One-half of the sum of numbers x and y.
Factorize `2x^2 + 3sqrt5x + 5`
(3x - 2 y)3 + (2 y - 4z )3 + (4z - 3x)3
Write the value of \[\left( \frac{1}{2} \right)^3 + \left( \frac{1}{3} \right)^3 - \left( \frac{5}{6} \right)^3 .\]
Multiply: (2x + 3y)(2x + 3y)
Divide: 8m - 16 by - 8
Divide: 8a2 + 4a - 60 by 2a - 5
The variable in the expression 16x – 7 is __________
Match Column I with Column II in the following:
| Column I | Column II |
| 1. The difference of 3 and a number squared | (a) 4 – 2x |
| 2. 5 less than twice a number squared | (b) n2 – 3 |
| 3. Five minus twice the square of a number | (c) 2n2 – 5 |
| 4. Four minus a number multiplied by 2 | (d) 5 – 2n2 |
| 5. Seven times the sum of a number and 1 | (e) 3 – n2 |
| 6. A number squared plus 6 | (f) 2(n + 6) |
| 7. 2 times the sum of a number and 6 | (g) 7(n + 1) |
| 8. Three less than the square of a number | (h) n2 + 6 |
In the term 10xyz, what is the numerical coefficient?
