Question

Factorise:
${a}^{6} + \frac{1}{ {a}^{6} } + 2.$

Answer 1

a^6[/tex]+$\frac{1}{a^{6} }$+2$( a^{3})( \frac{1}{ a^{3} )$
=$( a^{3}+ \frac{1}{a^{3} })^{2}$

Answer 2

Hope u like my process
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Formula to be used ::
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=> x² + y² +2xy = (x+y) ²

=> x³ + y³ = (x+y) (x² - xy +y²)
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${a}^{6} + \frac{1}{ {a}^{6} } + 2 \\ \\ = {( {a}^{3} )}^{2} + {( \frac{1}{ {a}^{3} } )}^{2} + 2 \times {a}^{3} \times \frac{1}{ {a}^{3} } \\ \\ = {( {a}^{3} + \frac{1}{ {a}^{3} }) }^{2} \\ \\ = {( {(a)}^{3} + {( \frac{1}{a}) }^{3} ) }^{2} \\ \\ = {((a + \frac{1}{a} )( {a}^{2} + \frac{1}{ {a}^{2} } - a \times \frac{1}{a} )) }^{2} \\ \\ = {((a + \frac{1}{a} )( {a}^{2} + \frac{1}{ {a}^{2} } - 1)) }^{2} \\ \\ = {(a + \frac{1}{a}) }^{2} {( {a}^{2} + \frac{ 1 }{ {a}^{2} } - 1) }^{2}$
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Hope this is ur required answer

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