Which of the following polynomials represents a difference of squares? x^2-1,x^2-8,4x^2+16,9x^2-18

Answer:[tex]x^{2} -1[/tex]Step-by-step explanation:we know thatEvery 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 casecase 1) we have[tex]x^{2} -1[/tex]In this case both numbers are perfect squareso[tex]x^{2} -1=(x+1)(x-1)[/tex]thereforeThe polynomial represent a difference of squarescase 2) we have[tex]x^{2} -8[/tex]In this case 8 is not a perfect squarethereforeThe polynomial not represent a difference of squarescase 3) we have[tex]4x^{2} +16[/tex][tex]4x^{2}+16=4(x^{2}+4)[/tex]In this case both numbers are perfect squarebut is a sum of squaresthereforeThe polynomial not represent a difference of squarescase 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 squarethereforeThe polynomial not represent a difference of squares