Answer: The completely factored form is :
[tex]y(x-\sqrt{5})(x+\sqrt{5})(x-i)(x+i)[/tex]
Step-by-step explanation:
Since we have given that
[tex]x^4y-4x^2y-5y[/tex]
We just need to simplify the above expression:
1) Take the common factor 'y' from the expression:
[tex]x^4y-4x^2y-5y\\\\=y(x^4-4x^2-5)[/tex]
2) Split the middle term :
[tex]y(x^4-4x^2-5)\\\\=y(x^4-5x^2+1x^2-5)\\\\=y(x^2(x^2-5)+1(x^2-5))\\\\=y(x^2-5)(x^2+1)\\\\[/tex]
3) Completely factored form:
[tex]y(x^2-5)(x^2+1)\\\\y(x-\sqrt{5})(x+\sqrt{5})(x-i)(x+i){\text{\{using }a^2-b^2=(a-b)(a+b)\}[/tex]
Hence, the completely factored form is :
[tex]y(x-\sqrt{5})(x+\sqrt{5})(x-i)(x+i)[/tex]
