If the sum of odd numbered terms and the sum of even numbered terms in the expansion of $(x + a)^{n}$ are $A$ and $B$ respectively, then the value of $(x^{2} - a^{2})^{n}$ is

A^{2} - B^{2}

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

A^{2} + B^{2}

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

4 A B

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

None

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

Open in App

Solution

The correct option is A $A^{2} - B^{2}$
$(x + a)^{n} =^{n} C_{0} x^{n} +^{n} C_{1} x^{n - 1} a +^{n} C_{2} x^{n - 2} a^{2} +^{n} C_{3} x^{n - 3} a^{3} +^{n} C_{4} x^{n - 4} a^{4} + . . . . .$
$= (^{n} C_{0} x^{n} +^{n} C_{2} x^{n - 2} a^{2} +^{n} C_{4} x^{n - 4} a^{4} + . . . . .) + (^{n} C_{1} x^{n - 1} a +^{n} C_{3} x^{n - 3} a^{3} +^{n} C_{5} x^{n - 5} a^{5}) + . . . .$
$= A + B$ .... (1)
Similarly, $(x - a)^{n} = A - B$ .... (2)
Multiplying eqns. (1) and (2), we get
$(x^{2} - a^{2})^{n} = A^{2} - B^{2}$

Suggest Corrections

Similar questions

Q. If the sum of odd numbered terms and the sum of even numbered terms in the expansion of

{(x + a)}^{n}

are A and B respectively, then the value of

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

is
(a)

A^{2} - B^{2}

(b)

A^{2} + B^{2}

If the sum of odd numbered terms and the sum of even numbered terms in the expansion of $(x + a)^{n}$ are A and B respectively, then the value of $(x^{2} - a^{2})^{n}$ is

Q. If

A

is the sum of the odd terms and

B

the sum of even terms in the expansion of

{(x + a)}^{n}

, then

A^{2} - B^{2} =

Q. If

A

be the sum of the odd terms and

B

the sum of the even terms in the expansion of

{(x + a)}^{n}

, prove that

A^{2} - B^{2} =

Q. If sum of odd terms is A and sum of even terms is B in the expansion

(x + a)^{n}

, then

Join BYJU'S Learning Program

If the sum of odd numbered terms and the sum of even numbered terms in the expansion of (x+a)n are A and B respectively, then the value of (x2−a2)n is

The correct option is A A2−B2(x+a)n=nC0xn+nC1xn−1a+nC2xn−2a2+nC3xn−3a3+nC4xn−4a4+.....=(nC0xn+nC2xn−2a2+nC4xn−4a4+.....)+(nC1xn−1a+nC3xn−3a3+nC5xn−5a5)+....=A+B .... (1)Similarly, (x−a)n=A−B .... (2)Multiplying eqns. (1) and (2), we get(x2−a2)n=A2−B2

If the sum of odd numbered terms and the sum of even numbered terms in the expansion of $(x + a)^{n}$ are $A$ and $B$ respectively, then the value of $(x^{2} - a^{2})^{n}$ is