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Question

The expression xnynx2y2 is equal to
(where x2y2 and n is even natural number greater than 6)

A
xn1+xn3y2+...+yn2
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B
xn2+xn4y2+...+yn2
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C
xn1+xn2y2+...+yn1
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D
xn2xn4y2+...yn2
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Solution

The correct option is B xn2+xn4y2+...+yn2
Let n=2m, mZ
Then xnynx2y2=(x2)m(y2)mx2y2

Let x2=a, y2=b

=(ab)(am1+am2b+...+bm1)ab
=am1+am2b+...+bm1
=xn2+xn4y2+...+x2yn4+yn2

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