Question

factorise x⁸+25x²+625​

Answer 1

Answer

Using the identity a

2

−b

2

=(a+b)(a−b)

Using the above identity, the expression x

4

−625 can be factorised as follows:

x

4

−625=(x

2

)

2

−(25)

2

=(x

2

−25)(x

2

+25)=(x−5)(x+5)(x

2

+25)

Hence, x

4

−625=(x−5)(x+5)(x

2

+25)

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