Question

(y-6/y)(y2+6+36/y2)​

Answer 1

Given:-

$(y - \frac{6}{y} )( {y}^{2} + 6 + \frac{36}{ {y}^{2} } )$

TO FIND:-

product using suitable identity

SOLUTION:-

use property:-

$( {a}^{3} - {b}^{3} ) = (a - b)( {a}^{2} + ab + {b}^{2} )$

here, a=x and b = $\frac{6}{y}$

$\therefore (y - \frac{6}{y} )( {y}^{2} + 6 + \frac{36}{ {y}^{2} } ) = {y}^{3} - { (\frac{6}{y}) }^{3}$

hence, product of

$\boxed{(y - \frac{6}{y} )( {y}^{2} + 6 + \frac{36}{ {y}^{2} } ) = {y}^{3} - ( \frac{6}{y} {)}^{3} }$

Answer 2

Given :  ( y - 6/y) (y²  + 6 + 36/y²)

To Find : product using suitable identities

Solution:

( y - 6/y) (y²  + 6 + 36/y²)

36/y²  can be written as  (6/y)²

=  ( y - 6/y) (y²  + 6 + (6/y)²)

6 can be written as   y * 6/y

=  ( y - 6/y) (y²  + y*6/y + (6/y)²)

(a - b)(a² + ab + b²) = a³ - b³

a = y

b = 6/y

=  y³ - (6/y)³

= y³ - 216/y³

( y - 6/y) (y²  + 6 + 36/y²) = y³ - 216/y³

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