stextFactorise the expression- 1 -x - 2-lfrac1 x - 2-2-2 x - lfrac 2 x A- x-1-xx-1-x-2B- x -1- x x -1- y -2C- x -1- x x -1- x -2D- x-1-xx-1-x-2

The correct option is D (x+1/x)(x+1/x 2)Given: x^2+1/x^2+2 2x 2/x Combining the first three terms and last two terms we get, =(x^2+1/x^2+2) (2x+2/x) Apply ...

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Byju's Answer

Standard VIII

Mathematics

Factorisation Using Algebraic Identities

stextFactoris...

Question

$Factorise the expression: x^{2} + \frac{1}{x^{2}} + 2 - 2 x - \frac{2}{x}$

(x + \frac{1}{x}) (x - \frac{1}{x} - 2)

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(x - \frac{1}{x}) (x - \frac{1}{x} - 2)

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(x - \frac{1}{x}) (x + \frac{1}{x} - 2)

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(x + \frac{1}{x}) (x + \frac{1}{x} - 2)

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Solution

The correct option is D $(x + \frac{1}{x}) (x + \frac{1}{x} - 2)$
$Given: x^{2} + \frac{1}{x^{2}} + 2 - 2 x - \frac{2}{x}$

$Combining the first three terms and last two terms we get, = (x^{2} + \frac{1}{x^{2}} + 2) - (2 x + \frac{2}{x})$

$Applying the identity (a + b)^{2} = a^{2} + 2 a b + b^{2} we get, (x^{2} + \frac{1}{x^{2}} + 2) = (x + \frac{1}{x})^{2} .$

$S o, (x^{2} + \frac{1}{x^{2}} + 2) - (2 x + \frac{2}{x}) = (x + \frac{1}{x})^{2} - 2 (x + \frac{1}{x})$

$Taking (x + \frac{1}{x}) common, we get,$

$(x + \frac{1}{x}) (x + \frac{1}{x} - 2)$

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Similar questions

\int \frac{e^{\sqrt{x}}}{\sqrt{x}} . (x + \sqrt{x}) d x

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Q. Show that for any non-zero rational number

x

, the following relation holds true:

1 + \frac{x}{2} + \frac{x (x - 1)}{2.4} + \frac{x (x - 1) (x - 2)}{2.4.6} + . . . . = 1 + \frac{x}{3} + \frac{x (x + 1)}{3.6} + \frac{x (x + 1) (x + 2)}{3.6.9} + . . . .

Q. Reduce the expression into lowest form:

\frac{x (x + 1)}{x - 2} \times \frac{1}{\frac{x}{(x + 1) (x - 2)}}

Q. Solve for

x \frac{x - 1}{2 x + 1} + \frac{2 x + 1}{x - 1} = 2

where

x \neq \frac{- 1}{2}, 1

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Factorise the expression: x2+1x2+2−2x−2x

$Factorise the expression: x^{2} + \frac{1}{x^{2}} + 2 - 2 x - \frac{2}{x}$