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
Answer: Option A
:
A
Let two numbers be a and b.
The difference of their cubes isa3–b3 and hence this is the expression we need.
This expression can be factorised asa3–b3=(a−b)(a2+ab+b2).
Now, consider the given factor, x4+x2y+y2=(x2)2+x2y+(y)2
This is in the form of a2+ab+b2where a=x2,b=y, which is similar to the factor given.
Therefore, the other factor is of the form a–b.
Hence, other factoris x2−y.
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:
A
Let two numbers be a and b.
The difference of their cubes isa3–b3 and hence this is the expression we need.
This expression can be factorised asa3–b3=(a−b)(a2+ab+b2).
Now, consider the given factor, x4+x2y+y2=(x2)2+x2y+(y)2
This is in the form of a2+ab+b2where a=x2,b=y, which is similar to the factor given.
Therefore, the other factor is of the form a–b.
Hence, other factoris x2−y.
Was this answer helpful ?
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