Question

factorize :x⁴-256
thanks​

Answer 1

Answer :

This is a difference of squares:

x^4 - 256 = (x^2)^2 - (16)^2 = (x^2 + 16)(x^2 - 16)

Now, we have difference of squares on the right factor again since x^2 - 16 = x^2 - 4^2.

Therefore, it can be factored as:

(x^2 + 16)(x - 4)(x + 4)

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Answer 2

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GIVEN :-

x⁴ - 256

TO FIND :-

Factorize

SOLUTION :-

x⁴−256

Recall; 

16²=256

∴x4−16²

x²(2)−16²

Recall; 

x²−y²=(x+y)(x−y)→difference of two squares

x²(2)−16²=(x²+16)(x²−16)

Factoring; x²−16=(x+4)(x−4)

Therefore;

x²+16(x+4)(x−4)

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