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Q.

What will be the factors of 10 x 4 y−10x y 4 ?


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a

9xy(x−y) x 2 +xy+ y 2

b

10xy(x−y) x 2 +xy+ y 2

c

15xy(x−y) x 2 +xy+ y 2

d

20xy(x−y) x 2 +xy+ y 2  

answer is B.

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Detailed Solution

We have to find the factors of 10 x 4 y−10x y 4 .
We know that,
a 3 − b 3 =(a−b) a 2 +ab+ b 2 Considering 10x4y-10xy4,
Taking out the common term in both terms,
10 x 4 y−10x y 4 =10xy x 3 − y 3 . . . (1)
Comparing (1) with a 3 − b 3 ,
a=x b=y
Factoring the expression (1),  10xy(x3-y3)=10xy(x-y)(x2+xy+y2)
Thus, the factors are 10xy(x-y)(x2+xy+y2).
Therefore, option 2 is correct.
 
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