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Question

If (x4+x2y+y2) is one of the factors of an expression which is the difference of two cubes, then the other factor is ___.


A
x2y
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B
x2y2
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C
xy2
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D
xy
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Solution

The correct option is A x2y

Let two numbers be a and b.
The difference of their cubes is a3b3 and hence this is the expression we need.

This expression can be factorised as a3b3=(ab)(a2+ab+b2).

Now, consider the given factor, x4+x2y+y2=(x2)2+x2y+(y)2

This is in the form of a2+ab+b2 where a=x2,b=y, which is similar to the factor given.

Therefore, the other factor is of the form ab.

Hence, other factor is x2y.


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