The product y -1- y y -1- y can be simplified asA- 2 yB- y 2-1- y 2C- 2 y 2D- y2-1-y2

The correct option is D y^2 1/y^2 (y+1/y ) ( y 1/y) = y ( y 1/y) + 1/y ( y 1/y) = y^2 1+1 1/y^2 = y^2 1/y^2 ...

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Byju's Answer

Standard VIII

Mathematics

Application of Algebraic Identities

The product y...

Question

The product ( $y$ + $\frac{1}{y}$ ) ( $y$ - $\frac{1}{y}$ ) can be simplified as _______.

2 $y$

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$y^{2}$ + $\frac{1}{y^{2}}$

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2 $y^{2}$

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$y^{2}$ - $\frac{1}{y^{2}}$

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Solution

The correct option is D
$y^{2}$ - $\frac{1}{y^{2}}$

( $y$ + $\frac{1}{y}$ ) ( $y$ - $\frac{1}{y})$

= $y$ ( $y$ - $\frac{1}{y})$ + $\frac{1}{y}$ ( $y$ - $\frac{1}{y})$

= $y^{2}$ -1+1 - $\frac{1}{y^{2}}$

= $y^{2}$ - $\frac{1}{y^{2}}$

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Similar questions

$(\frac{1}{x} + \frac{1}{y}) (\frac{1}{x} - \frac{1}{y}) = ?$
(a) $(\frac{1}{x^{2}} - \frac{1}{y^{2}})$
(b) $(\frac{1}{x^{2}} + \frac{1}{y^{2}})$
(c) $(\frac{1}{x^{2}} + \frac{1}{y^{2}} - \frac{1}{x y})$
(d) $(\frac{1}{x^{2}} - \frac{1}{y^{2}} + \frac{1}{x y})$

Simplify

(y²-y-1)-(½(x-1+2x))

Q. Simplify:

(1 + \frac{x^{2} - y^{2} - z^{2}}{2 y z}) (\frac{1}{x + y - z} + \frac{1}{z + x - y})

If y = ${log}_{x}$ 2. Find the value of ${log}_{4}$ x.

Q. The factors of x³ − 1 + y³ + 3xy are

(a) (x − 1 + y) (x² + 1 + y² + x + y − xy)

(b) (x + y + 1) (x² + y² + 1 −xy − x − y)

(c) (x − 1 + y) (x² − 1 − y² + x + y + xy)

(d) 3(x + y −1) (x² + y² − 1)

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The product ( y + 1y ) ( y - 1y ) can be simplified as _______.

The correct option is D y2 - 1y2 (y+1y ) ( y -1y) = y ( y - 1y) + 1y ( y - 1y) = y2 -1+1 -1y2 = y2 - 1y2

The product ( $y$ + $\frac{1}{y}$ ) ( $y$ - $\frac{1}{y}$ ) can be simplified as _______.

The correct option is D
$y^{2}$ - $\frac{1}{y^{2}}$

( $y$ + $\frac{1}{y}$ ) ( $y$ - $\frac{1}{y})$

= $y$ ( $y$ - $\frac{1}{y})$ + $\frac{1}{y}$ ( $y$ - $\frac{1}{y})$

= $y^{2}$ -1+1 - $\frac{1}{y^{2}}$

= $y^{2}$ - $\frac{1}{y^{2}}$