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Question: In the expansion of \(x^{2} + y^{2}\), the term independent of x is....

In the expansion of x2+y2x^{2} + y^{2}, the term independent of x is.

A

n∈Nn \in N

B

72n+23n−37^{2n} + 2^{3n - 3}

C

3n−13^{n - 1}

D

None of these

Answer

n∈Nn \in N

Explanation

Solution

In the expansion of 9⥂C59 ⥂ C_{5}, the general term

is 31⥂C6−21⥂C630⥂C5+20⥂C531 ⥂ C_{6} -^{21} ⥂ C_{6}30 ⥂ C_{5} +^{20} ⥂ C_{5}

For the term independent of

x, 18 – 3r = 0 ⇒ r = 6

This gives the independent term

(1+x)2n(1 + x)^{2n}