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General Term of Binomial Expansion

If T 0, T 1, ...

Question

If $T_{0}, T_{1}, T_{2}, . . . . . . . . . . . . . . . . . . T_{n}$ represent the terms in the expansion of $(x + a)^{n}$ , then the value of $(T_{0} - T_{2} + T_{4} - T_{6} + . . . . . . . . . . . . . . . . .)^{2}$ + $(T_{1} - T_{3} + T_{5} - . . . . . . . . . . . . . . . . .)^{2}$ is

A

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B

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C

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D

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Solution

The correct option is B

$T_{r + 1} =^{n} C_{r} x^{n - r} . a^{r}$

$(x + a i)^{n} =^{n} C_{0} x^{n} +^{n} C_{1} x^{n - 1} . a . i +^{n} C_{2} x^{n - 2} a^{2} . i^{2} + . . . . . . .$ = $(T_{0} - T_{2} + T_{4} - T_{6} + . . . . . . . . . . . . . . . . .)$ + $(T_{1} - T_{3} + T_{5} - . . . . . . . . . . . . . . . . .)$

$(T_{0} - T_{2} + T_{4} - T_{6} + . . . . . . . . . . . . . . . . .)^{2}$ + $(T_{1} - T_{3} + T_{5} - . . . . . . . . . . . . . . . . .)^{2} = (x^{2} + a^{2})^{n}$

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Similar questions

T_{0}, T_{1}, T_{2}, . . . . T_{n}

represent the terms in the expansion of

{(x + a)}^{n}

, then the value of

{(T_{0} - T_{2} + T_{4} - T_{6} + . . . .)}_{0}^{2}

{(T_{1} - T_{3} + T_{5} - . . . .)}_{1}^{2}

T_{0}, T_{1}, T_{2}, \dots T_{n}

represent the terms in the expansion of

(x + a)^{n}

, then the value of

(T_{0} - T_{2} + T_{4} - T_{6} + \dots)^{2} + (T_{1} - T_{3} + T_{5} - \dots)^{2}

T_{0}, T_{1}, T_{2}, . . . . . T_{n}

represent the term in the expansion of

(x + a)^{n}

, then the value of

(T_{0} - T_{2} + T_{4} - T_{6} + . . . . .)^{2} + (T_{1} - T_{3} + T_{5} + . . . . .)^{2}

T_{0}, T_{1}, T_{2}, . . ., T_{n}

represent in the terms in the expansion of

{(x + a)}^{n}

, then the value of

{(T_{0} - T_{2} + T_{4} - T_{6} + . . .)}_{0}^{2} + {(T_{1} - T_{3} + T_{5} + . . .)}_{1}^{2}

t_{0}, t_{1}, t_{2}, t_{n}

are the consecutive terms in the expansion

(x + a i)^{n}

(t_{0} - t_{2} + t_{4} - t_{6} + \dots .)^{2} + (t_{1} - t_{3} + t_{5} \dots .)^{2} =

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