Question

Evaluate the product ( a -1/a)(a+1/a)(a^2+1/a^2) for a = -2.​

Answer 1

Step-by-step explanation:

$\bold \color{red}{ \mathfrak{question : }}$

$= (a - \frac{1}{a} )(a + \frac{1}{a} )( {a}^{2} + \frac{1}{ {a}^{2} } ) \: \: \: for \: a = - 2$

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

kindly use( if it's important ) "{}" (curly brackets) after the parentheses are used.

$= ( - 2+ \frac{1}{2} )( - 2 - \frac{1}{2} )(4 + \frac{1}{4} )$

now take LCM of every denominators in each brackets( parentheses ).

$= ( \frac{ - 2 \times 2 + 1}{2} )( \frac{ - 2 \times 2 - 1}{2} )( \frac{4 \times 4 + 1}{4} )$

$= ( \frac{ - 4 + 1}{2} )( \frac{ - 4 - 1}{2} )( \frac{16 + 1}{4} )$

$= ( \frac{ - 3}{2} )( \frac{ - 5}{2} )( \frac{17}{4} )$

$= \frac{15 \times 17}{4 \times 4}$

$= \frac{255}{16}$

$(a - \frac{1}{a} )(a + \frac{1}{a} )( {a}^{2} + \frac{1}{ {a}^{2} } ) \: \: for \: a = - 2 \implies \bold{\frac{255}{16} }$