How+to+Factor+a+Difference+of+Squares

What is a perfect square?

 * A perfect square is a term that has a regular square root.

When do you use difference of squares?

 * You can only use difference of squares when there is a binomial with two perfect squares separated by a subtraction sign.

Steps to Finding Difference of Squares

 * 1) Check to be sure there are no common factors but that there are two perfect squares separated by a subtraction sign.
 * 2) Find the square root of each term.
 * 3) You will use the equation a 2 - b 2 = (a+b)(a-b). The two signs must be opposites to cancel out a third term.
 * 4) Check your answer using FOIL.*


 * //If you have troubles with FOIL, see link below.//

Examples
25x 2 - 36 Let's go through the steps.

1. 25x 2 and 36 are perfect squares and are separated by a subtraction sign with no common factors in the equation, next step.
2. The square root of 25x 2 is 5x. The square root of 36 is 6. 3. Plug the numbers into the equation. a=5x b=6 So, our answer is (5x+6)(5x-6) 4. When we foil (5x+6)(5x-6) we get 25x2 - 30x + 30x - 36. The -30x and the +30x cancel each other out, so we are left with a binomial, 25x 2 - 36.

81x 2 - 49 1. 81x 2 and 49 are perfect squares, separated by a subtraction sign, and don't have any common factors. 2. The square root of 81x 2 is 9x and the square root of 49 is 7. 3. a=9x and b=7 When we plug these numbers into the equation we get (9x+7)(9x-7) 4. When we foil and simplify the equation we end up with 81x 2 - 49