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Question

Resolve into factors: x46x2y2+y4

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Solution

In the given expression x4+y46x2y2, add and subtract 2x2y2 to make it a perfect square as shown below:

x4+y46x2y2=(x4+y4+2x2y2)6x2y22x2y2=(x2+y2)28x2y2
(using the identity (a+b)2=a2+b2+2ab

We also know the identity a2b2=(a+b)(ab), therefore,

Using the above identity, the equation (x2+y2)28x2y2can be factorised as follows:

(x2+y2)28x2y2=(x2+y2)2(8xy)2=(x2+y2+8xy)(x2+y28xy)

Hence, x4+y46x2y2=(x2+y2+8xy)(x2+y28xy)


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