


Factoring A Difference Between Two SquaresTake a look at the problem (expression) below: 4x^{2}  16 The first step at factoring this is to make sure that the expression is a difference between squares.
Because "Yes" was answered to each of the above questions, we know that the expression is a difference between two squares. Begin the factoring process by writing two sets of open parentheses: ( )( ) Now find the square root of 4x^{2}, the first term, by finding the square root of 4 and then dividing each exponent by 2. The square root of 4 is 2. Half of the exponent 2 is 1, thus x^{2} becomes x^{1} or x. Thus, the square root of the entire term is 2x. Write this term on the left inside of each set of parentheses. (2x )(2x ) We will now consider 16, the second term without the negative sign. We will apply the same process that we applied to 4x^{2}. There are no variables in 16, so we simply find that the square root of 16 is 4. Now 4 is written on the right inside of each set of parentheses. (2x 4)(2x 4) Add a plus sign to the middle of the first set of parentheses, then add a minus sign to the middle of the second set of parentheses. (2x + 4)(2x  4) The result is two parentheses which can be multiplied to get the original expression 4x^{2}  16. To check that this answer is correct, you can apply the FOIL Method which was presented in an earlier lesson. Proceed to the next page to see another example of factoring a Difference Between Two Squares. 

