Question

please answer this question​

Answer 1

Answer:

your final answer should be x4-1/x4

Answer 2

Answer:

$\color{green} = \tt {x}^{4} - \frac{1}{ {x}^{4} }$

Step-by-step explanation:

$\huge{ \tt \: solution : }$

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

$\tt = \bigg[( {x}^{2}) - \bigg ( \frac{1}{ {x}^{2} } \bigg)\bigg ] \bigg( {x}^{2} + \frac{1}{ {x}^{2} } \bigg)$

$\color{blue} \tt \bigg [because \: (a + b)(a - b) = {a}^{2} - {b}^{2} \\ \color{blue} \tt and \:above \: a = x \: and \: b = \frac{1}{x} \bigg]$

$\tt \: = \bigg( {x}^{2} - \frac{1}{ {x}^{2} } \bigg) \bigg( {x}^{2} + \frac{1}{ {x}^{2} } \bigg)$

$\tt = \bigg ( {x}^{2} - \frac{1}{ {x}^{2} } \bigg) \bigg( {x}^{2} + \frac{1}{ {x}^{2} } \bigg)$

$\tt = ( {x}^{2} {)}^{2} - \bigg( \frac{1}{ {x}^{2} } { \bigg)}^{2}$

$\color{lightblue} \tt \bigg[ because \: (a + b)(a - b) = {a}^{2} - {b}^{2} \: and \\ \color{lightblue} \tt \: above \: a = {x}^{2} \: and \: b = \frac{1}{ {x}^{2} } \bigg]$

$\tt = {x}^{2 \times 2} - \frac{( {1)}^{2} }{( {x}^{2} {)}^{2} }$

$\tt = {x}^{4} - \frac{1}{ {x}^{2 \times 2} }$

$\tt = {x}^{4} - \frac{1}{ {x}^{4} }$

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$\huge \tt \: identity \: used : - -$

$\tt( a + b)(a - b)$