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If T0,T1, T2,.....Tn represent the terms...

If `T_0,T_1, T_2,.....T_n` represent the terms in the expansion of `(x+a)^n ,` then find the value of `(T_0-T_2+T_4-....)^2+(T_1-T_3+T_5-.....)^2n in Ndot`

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`(x-a)^(n) = .^(n)C_(0)x^(n) + .^( n)C_(1)x^(n-1)a+.^(n)C_(2)x^(n-2)a^(2)+.^(n)C_(3)x^(n-3)a^(3)+"…."`
`= T_(0) + T_(1) + T_(2) + T_(3) + "……"`
Repalcing a by ai, we get
`(x+ai)^(n) = .^(n)C_(0)x^(n) + .^(n)C_(1)x^(n-1)ai + .^(n)C_(2)x^(n-2)(ai)^(2) + .^(n)C_(3)x^(n-3) (ai)^(3) + "....."`
` = (.^(n)C_(0)x^(n)-.^(n)C_(1)x^(n-2)a^(2) + .^(n)C_(4)x^(n-4)a^(4)-"......") + i(.^(n)C_(1)x^(n)a-.^(n)C_(3)x^(n-3)a^(3)+.^(n)C_(5)x^(n-5)a^(5)-"......")`
` = (T_(0) - T_(2) + T_(4) - ".....") + i(T_(1) - T_(3) + T_(5)-".....")`
Taking modulus of both sides and squaring, we get
`|x+ai|^(2n)=|(T_(0)-T_(2)+T_(4)-".......") + i(T_(i ) - T_(3) + T_(5) - ".....")|^(2)`
or `(x^(2)+a^(2))^(n) = (T_(0) - T_(2) + T_(4)-"......")^(2)+(T_(1) - T_(3) + T_(5) -"......")^(2)`
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