Advertisements
Advertisements
प्रश्न
Factorize the following expressions:
`a^3 - 1/a^3 - 2a + 2/a`
Advertisements
उत्तर
`= (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
संबंधित प्रश्न
Factorize the following expressions:
10x4y – 10xy4
a3 + 8b3 + 64c3 - 24abc
`2sqrt2a^3 + 16sqrt2b^3 + c^3 - 12abc`
If a + b + c = 0, then write the value of a3 + b3 + c3.
If (x + y)3 − (x − y)3 − 6y(x2 − y2) = ky2, then k =
Evaluate: (a2 + 2ab + b2)(a + b)
Multiply: (2x - 3y)(2x + 3y)
Divide: 8x + 24 by 4
Write the coefficient of x2 and x in the following polynomials
πx2 – x + 2
In the given figure, the length of a green side is given by g and that of the red side is given by p.
Write an expression for the following pattern. Also write an expression if 100 such shapes are joined together.
