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Quantitative Aptitude Question on Algebra

What is the value of (x4+y4+x2y2)x2−2xy+y2x2−xy+y2÷(x3−y3)(x^4+y^4+x^2y^2)\frac{x^2-2xy+y^2}{x^2-xy+y^2}\div(x^3-y^3) ?

A

(x - y)/(x + y)

B

(x + y)/(x - y)

C

x + y

D

x - y

Answer

x - y

Explanation

Solution

We know, (a - b)2 = a2 - 2ab + b2
a4 + b4 + a2b2 = (a2 - ab + b2)(a2 + ab + b2)
a3 - b3 = (a - b)(a2 + ab - b2)
Then, (x4+y4+x2y2)x2−2xy+y2x2−xy+y2÷(x3−y3)(x^4+y^4+x^2y^2)\frac{x^2-2xy+y^2}{x^2-xy+y^2}\div(x^3-y^3)
=(x4+y4+x2y2)x2−2xy+y2x2−xy+y2(1x3−y3)=(x^4+y^4+x^2y^2)\frac{x^2-2xy+y^2}{x^2-xy+y^2}(\frac{1}{x^3-y^3})
=(x2−xy+y2)(x2+xy+y2)(x−y)2x2−xy+y2(1(x−y)(x2+xy+y2))=(x^2-xy+y^2)(x^2+xy+y^2)\frac{(x-y)^2}{x^2-xy+y^2}(\frac{1}{(x-y)(x^2+xy+y^2)})
= x - y
So, the correct option is (D) : x - y.