Factoring Polynomials: The difference of two squares
When factoring polynomials, the first step is always to look for common factors and to factor them out. After that, you can see if the polynomial can be factored further.
There is a special situation called the difference of two squares that has a special pattern for factoring. Here is the pattern: ![]() First, notice that there are three requirements that must be met in order for us to be able to use this pattern. 1) It must be a binomial (have two terms)
2) Both terms must be perfect squares (meaning that you could take the square root and they would come out evenly.) 3) There must be a subtraction/negative sign (not addition) in between them If these three requirements are met, then we can easily factor the binomial using the pattern. Simply... 1) Write two parenthesis 2) Put a ![]() ![]() 3) Take the square root of the first term and put that in the front of each parenthesis 4) Take the square root of the last term and put that in the back of each parenthesis As before, you can check your work by multiplying out your answer and making sure the result matches the original. Here's a couple examples:
1) ![]() continue on to check the criteria. It is a binomial with two perfect squares and subtraction, so we can use this pattern. ![]() ![]() front of each parenthesis. We take the square root of 25 which is 5 and put that in the back of each.
Final answer: ![]() distribute or use FOIL). We get
![]() 2) ![]() continue on to check the criteria. It is a binomial with two perfect squares and subtraction, so we can use this pattern. ![]() ![]() ![]() ![]() in the front of each parenthesis. We take the square root of 4x2 which is 2x and put that in the back of each. Final answer ![]() (remember to distribute or use FOIL). We get ![]() 3) ![]() ![]() ![]() Answer: ![]() We can check this by multiplying everything out. Let's distribute the 3 first: ![]() Practice: Factor the following. Check for common factors first then the difference of two squares. 1) ![]() 2) ![]() 3) ![]() 4) ![]() 5) ![]() Answers: 1) ![]() ![]() ![]() ![]() ![]() |
Related Links: Math Algebra Factors Polynomials Algebra Topics |