Evaluate `(sqrt(3)+sqrt(2))^6-(sqrt(3)-sqrt(2))^6dot`

Answer

N/a

Explanation

From the expansion of binomial theorem
`(sqrt(3))+sqrt(2))^(6)=^(6)C_(0)(sqrt(3))^(6)+^(6)C_(1)(sqrt(3))^(5)sqrt(2)`
`+^(6)C_(2)(sqrt(3))^(4)(sqrt(2))^(2)+^(6)C_(3)(sqrt(3))^(3)(sqrt(2))^(3)`
`+^(6)C_(4)(sqrt(3))^(2)(sqrt(2))^(4)+^(6)C_(5)sqrt(3)(sqrt(2))^(5)`
`+^(6)C_(6)(sqrt(2))^(6)`
`" and " (sqrt(3)-sqrt(2))^(6)=^(6)C_(0)(sqrt(3))^(6)-^(6)C_(1)(sqrt(3))^(5)sqrt(2)`
`+^(6)C_(2)(sqrt(3))^(4)(sqrt(2))^(2)-^(6)C_(3)(sqrt(3))^(3)(sqrt(2))^(2)`
`.^(6)C_(4)(sqrt(3))^(2)(sqrt(2))^(4)-^(6)C_(5)sqrt(3)(sqrt(2))^(5)]`
`=2[6xx9 sqrt(3)xxsqrt(2)+20xx30sqrt(3)`
`=2[54sqrt(6)+120sqrt(6)+249sqrt(6)]`
`=2xx 198 sqrt(6)`
`=296 sqrt(6)`
Therefore ,
`(sqrt(3))+sqrt(2))^(6)-(sqrt(3))-sqrt(2))^(6)=396sqrt(6)`