Question

Factorise the following equation :-
:$\mapsto \sf{x^(8) - x^(4) - 72}$
$\bold{ Need \: step \: by \: step \: explanation}$​

Answer 1

Step-by-step explanation:

Let x

4

=a.

Then x

8

−x

4

−72=a

2

−a−72

a

2

−9a+8a−72

=a(a−9)+8(a−9)

=(a−9)(a+8)

=(x

4

−9)(x

4

+8)

∵a

2

−b

2

=(a−b)(a+b)

=((x

2

)

2

−3

2

)(x

4

+8)=(x

2

−3)(x

2

+3)(x

4

+8)