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Factorize the expression $4 x 4 + y 4$ .

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2 x 2 + y 2 + 2 x y 2 x 2 + y 2 − 2 x y

2 x 2 + y 2 − 2 x y 2 x 2 + y 2 − 2 x y

2 x 2 − y 2 − 2 x y 2 x 2 + y 2 − 2 x y

None of these

answer is A.

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Detailed Solution

Given expression is

4 x 4 + y 4

.
Using the identity,

a + b 2 = a 2 + b 2 + 2 a b

Comparing the given expression with an identity,

4 x 4 + y 4 = 2 x 2 2 + y 2 2 + 4 x 2 y 2 − 4 x 2 y 2 ⇒ 4 x 4 + y 4 = 2 x 2 + y 2 2 − 4 x 2 y 2

Now, using the identity,

a 2 − b 2 = a + b a − b

So, the expression can be written as:

4 x 4 + y 4 = 2 x 2 + y 2 − 2 x y 2 ⇒ 4 x 4 + y 4 = 2 x 2 + y 2 + 2 x y 2 x 2 + y 2 − 2 x y

Therefore, the factors of the

4 x 4 + y 4

are

2 x 2 + y 2 + 2 x y and 2 x 2 + y 2 − 2 x y

.
Thus, the factorisation of

.
Hence, option 1 is correct.

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