How do you determine if a polynomial is the difference of two squares?

Question

How do you determine if a polynomial is the difference of two squares?

Answer 1

Step 1 - See if you have two terms in the polynomial (e.g. a binomial)

Step 2 - See if both terms are perfect squares (e.g. 49x²)

Step 3 - See if there is a subtraction sign (difference)

If you answer yes to all 3 you have a difference of squares.

Example:

49x² - 64

16a² - 25b²

16 - 4x²

P.S.  On step 2, a term is a perfect square if the coefficient (e.g. the number) is a perfect square, and then the variable(s) all have even powers.  4x²y^4 is a perfect square.  9a^4b^6 is a perfect square.  9c² is a perfect square.

Once you know you have two squares being subtracted you can use the rule for the difference of two squares.  In general:

a² - b² = (a - b)(a + b)

Using the examples above:

49x² - 64 = (7x - 8)(7x + 8)

16a² - 25b² = (4a - 5b)(4a + 5b)

16 - 4x² = (4 - 2x)(4 + 2x)