solve x power 4 - 81
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x^4 - 81
= (x^2)^2 -(9)^2
now, it is in the form of a^2 -b^2
then,
(x^2)^2 -(9)^2
= (x^2 + 9) (x^2 -9)
(x^2 -9)
= (x)^2 -(3)^2 ... it is also in the form of a^2 -b^2
so,
(x^2 + 9) (x^2 -9)
= (x^2 +9) ( x +3) (x-3)
so,
x^4 - 81 = (x^2 +9) ( x +3) (x-3)
= (x^2)^2 -(9)^2
now, it is in the form of a^2 -b^2
then,
(x^2)^2 -(9)^2
= (x^2 + 9) (x^2 -9)
(x^2 -9)
= (x)^2 -(3)^2 ... it is also in the form of a^2 -b^2
so,
(x^2 + 9) (x^2 -9)
= (x^2 +9) ( x +3) (x-3)
so,
x^4 - 81 = (x^2 +9) ( x +3) (x-3)
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