Question

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

Answer 1

Answer:

$x^{2} -1$

Step-by-step explanation:

we know that

Every difference of squares problem can be factored as follows:

$a^{2}-b^{2}=(a+b)(a-b)$

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

$x^{2} -1$

In this case both numbers are perfect square

so

$x^{2} -1=(x+1)(x-1)$

therefore

The polynomial represent a difference of squares

case 2) we have

$x^{2} -8$

In this case 8 is not a perfect square

therefore

The polynomial not represent a difference of squares

case 3) we have

$4x^{2} +16$

$4x^{2}+16=4(x^{2}+4)$

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

$9x^{2}-18$

$9x^{2}-18=9(x^{2}-2)$

In this case 2 is not a perfect square

therefore

The polynomial not represent a difference of squares