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

(x^{2} - a^{2})^{n}

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

(x^{2} + a^{2})^{n}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

(a^{2} - x^{2})^{n}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

none of these

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is A $(x^{2} - a^{2})^{n}$
Given
$T_{0}, T_{1}, T_{2}, . . . . . . . . . . . . . . ., T_{n}$ represent terms in expansion of $(x + a)^{n}$

$(x + a)^{n} = T_{0} + T_{1} + T_{2} + T_{3} + . . . . . . . . . + T_{n} - - - - - - - - - (1)$
When $a = - a$ we get
$(x - a)^{n} = T_{0} - T_{1} + T_{2} - T_{3} + . . . . . . . . . + (- 1)^{n} T_{n} - - - - - - (2)$

Multiplying eq (1) and (2) and comparing with terms $x^{r}$ we get
$(x + a)^{n} \cdot (x - a)^{n} = (T_{0} - T_{2} + T_{4} - T_{6} + . . . . . . . . .)^{2} + (T_{1} - T_{3} + T_{5} + . . . . . . . . .)^{2}$

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

Suggest Corrections

Similar questions

Q. 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} + . . . .)}_{0}^{2}

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

Q. If

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}

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

Q. If

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}

is equal to

Q.
lf

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

are the consecutive terms in the expansion

(x + a i)^{n}

, then

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

Join BYJU'S Learning Program

If T0,T1,T2,.....Tn represent the term in the expansion of (x+a)n, then the value of (T0−T2+T4−T6+.....)2+(T1−T3+T5+.....)2 is

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