Answer:
factoring the term [tex]x^4-1[/tex] we get [tex]\mathbf{(x^2+1)(x-1)(x+1}[/tex]
Step-by-step explanation:
We need to factor the term [tex]x^4-1[/tex]
We know that [tex]a^2-b^2=(a-b)(a+b)[/tex]
We can write [tex]x^4 \ as \ (x^2)^2[/tex]
Simplifying:
[tex]x^4-1\\=(x^2)^2-1\\=(x^2-1)(x^2+1)\\[/tex]
Now, again using formula [tex]a^2-b^2=(a-b)(a+b)[/tex]
[tex]=(x^2+1)((x)^2-1)\\=(x^2+1)(x-1)(x+1)[/tex]
So, factoring the term [tex]x^4-1[/tex] we get [tex]\mathbf{(x^2+1)(x-1)(x+1}[/tex]
