Advertisements
Advertisements
Question
Simplify:
`("a" + 1/"a")^3 - ("a" - 1/"a")^3`
Solution
`("a" + 1/"a")^3 - ("a" - 1/"a")^3`
= `("a")3 + (1/"a")^3 + 3("a")(1/"a")("a" + 1/"a") - [("a")^3 - (1/"a")^3 = -3("a")(1/"a")("a" - 1/"a")]`
= `"a"^3 + (1)/"a"^3 + 3("a" + 1/"a") - ["a"^3 - 1/"a"^3 - 3("a" - 1/"a")]`
= `"a"^3 + (1)/"a"^3 + 3"a" + (3)/"a" - "a"^3 + (1)/"a"^3 + 3"a" - (3)/"a"`
= `(2)/"a"^3 + 6"a"`.
APPEARS IN
RELATED QUESTIONS
Expand.
(k + 4)3
The sum of two numbers is 9 and their product is 20. Find the sum of their (i) Squares (ii) Cubes
Expand : (3x + 5y + 2z) (3x - 5y + 2z)
Find the cube of: `4"p" - (1)/"p"`
Find the cube of: `"a" - (1)/"a" + "b"`
If `"a" - (1)/"a" = 7`, find `"a"^2 + (1)/"a"^2 , "a"^2 - (1)/"a"^2` and `"a"^3 - (1)/"a"^3`
If `"p" + (1)/"p" = 6`; find : `"p"^3 + (1)/"p"^3`
If a + b = 5 and ab = 2, find a3 + b3.
Expand: (x + 3)3.
If `x^2 + 1/x^2` = 23, then find the value of `x + 1/x` and `x^3 + 1/x^3`
