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Question

x4y4 divided by x-y we get

A
(x+y)(x2+y2)
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B
x+y
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C
x2y2
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D
2y4
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Solution

The correct option is A (x+y)(x2+y2)
Let f(x)=x4y4 and factorise it as follows:

f(x)=x4y4=(x2y2)(x2+y2)=(xy)(x+y)(x2+y2)

Therefore, f(x)=(xy)(x+y)(x2+y2)

Let g(x)=xy

Now divide f(x) by g(x) to get q(x):

q(x)=(xy)(x+y)(x2+y2)(xy)=(x+y)(x2+y2)

Hence, the quotient q(x)=(x+y)(x2+y2).


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