Question

if x^4 + x^2y + y^2 is one of the factors of an expression which is the difference of two cubes then the other factor is x^2 - y.

Is it true or false?​

Answer 1

Answer:

TRUE

Step-by-step explanation:

As the given expression is the factor of and expression which is difference of cubes i.e, x³-y³=(x-y)(x²+xy+y2)

Hence multiply (x⁴+x²y+y²) and (x²-y) you'll be getting the final answer as x^6-y³

without any contradiction you can write it as (x²)³-y³

Therefore your required condition satisfies that the nos are difference of 2 cubes

I hope it helps

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Answer 2

Answer:

Yes it's absolutely TRUE

Step-by-step explanation:

Let two numbers be a and b.

The difference of their cubes is a3–b3 and hence this is the expression we need.

This expression can be factorized as a^3–b^3=(a−b)(a^2+ab+b^2).

Now, consider the given factor, x^4+x^2y+y^2=(x^2)^2+x^2y+(y)^2

This is in the form of a^2+ab+b^2 where a=x^2,b=y, which is similar to the factor given.  

Therefore, the other factor is  of the form a–b.    

Hence, other factor is x^2−y.