Question

(a-1/a)(a+1/a)(a^2+1/a^2)(a^4+1/a^4) simplify​

Answer 1

Step-by-step explanation:

$(a - \frac{1}{a} )(a + \frac{1}{a}) \: ({a}^{2} + \frac{1}{ {a}^{2} } )( {a}^{4} + \frac{1}{ {a}^{4} } ) \\ = (a^{2} - \frac{1}{a ^{2} } )( {a}^{2} + \frac{1}{ {a}^{2} } ) \: ( {a}^{4} + \frac{1}{a^{4} } ) \\ = ( {a}^{4} - \frac{1}{a ^{4} } )(a^{4} + \frac{1}{ {a}^{4} }) \\ = {a}^{8} - \frac{1}{ {a}^{8} }$

All the expansion use the common identity:-

(a + b)(a - b) = a² - b²

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Answer 2

Answer:

(a−

a

1

)(a+

a

1

)(a

2

+

a

2

1

)(a

4

+

a

4

1

)

=(a

2

−

a

2

1

)(a

2

+

a

2

1

)(a

4

+

a

4

1

)

=(a

4

−

a

4

1

)(a

4

+

a

4

1

)

=a

8

−

a

8

1

All the expansion use the common identity:-

(a + b)(a - b) = a² - b²