Answer:
[tex]x^{2} -1[/tex]
Step-by-step explanation:
we know that
Every difference of squares problem can be factored as follows:
[tex]a^{2}-b^{2}=(a+b)(a-b)[/tex]
If the polynomial represent a difference of squares every number must be a perfect square (Remember that a number is a perfect square if its square root is an integer.)
Verify each case
case 1) we have
[tex]x^{2} -1[/tex]
In this case both numbers are perfect square
so
[tex]x^{2} -1=(x+1)(x-1)[/tex]
therefore
The polynomial represent a difference of squares
case 2) we have
[tex]x^{2} -8[/tex]
In this case 8 is not a perfect square
therefore
The polynomial not represent a difference of squares
case 3) we have
[tex]4x^{2} +16[/tex]
[tex]4x^{2}+16=4(x^{2}+4)[/tex]
In this case both numbers are perfect square
but is a sum of squares
therefore
The polynomial not represent a difference of squares
case 4) we have
[tex]9x^{2}-18[/tex]
[tex]9x^{2}-18=9(x^{2}-2)[/tex]
In this case 2 is not a perfect square
therefore
The polynomial not represent a difference of squares
