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Find (x+1)^6+(x-1)^6. Hence or otherwise...

Find `(x+1)^6+(x-1)^6`. Hence or otherwise evaluate `(sqrt(2)+1)^6+(sqrt(2)-1)^6`.

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The correct Answer is:
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`(x+1)^(6)+(x-1)^(6)`
`=overset(6)underset(r=0)(Sigma).^(6)C_(r)X^(6-r).(1)^(r)+overset(6)underset(r=0)(Sigma).^(6)C_(r)x^(6-r)(-1)^(r)`
`=(.^(6)C_(0).x^(6)+^(6)C_(1).x^(5)+^(6)C_(2).x^(4)+^(6)C_(3).x^(3)`
`+^(5)C_(4).x^(2)+^(6)C_(5).x+^(6)C_(6))+(.^(6)C_(0).x^(6-6)C_(1).x^(5)`
`+^(6)C_(4).x^(4)-^(6)C_(3).x^(3)+^(6)C_(4).x^(2)-^(6)C_(5).x+^(6)C_(6))`
`=2.[.^(6)C_(0).x^(6)+^(6)C_(2).x^(4)+^(6)C_(4).x^(2)+^(6)C_(6)]`
`=2(x^(6)+15x^(4)+15x^(2)+1)`
`" Put " x=sqrt(2),`
`(sqrt(2))+1)^(6)+(sqrt(2))-1)^(6)`
`=2[(sqrt(2))^(6)+15(sqrt(2))^(4)+15(sqrt(2))^(2)+1]`
`=2[8+60+30+1]=198`
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