Factoring Difference of Squares #2
Description/Explanation/Highlights
Video Description
In this video the method for factoring the difference of two squares with a coefficient other than 1 is explained.
Steps and Key Points to Remember
To factor the difference of two perfect squares when the lead coefficient is also a perfect square other than 1, follow these steps:
- Before starting, make sure all numbers and variables in both terms are perfect squares. In the example \(25x^2-36\) all of the numbers and variables in both terms of the expression are perfect squares. i.e. \(25=5\cdot 5\text{ } x^2 = x \cdot x\) and \(36 = 6 \cdot 6\)
- As with perfect squares with a lead coefficient of 1, make sure the operation is subtractions. Remember, you cannot factor the sum of squares.
- The difference of squares will factor into two binomials (two terms) with two sets of parenthesis.
i.e. ( ) ( ) - At this point, find the square root of the first term. In other words, what number or variable multiplied by itself will give you the first term. In our example \(\sqrt{25x^2}=5x\)
- Therefore, 5x is the first term of each binomial
i.e. (5x )(5x ) - Repeat the process and find the square root of the second term. In our example \(\sqrt{36}=6\)
- 6 is the second term of each binomial
i.e. (5x 6)(5x 6) - Now put a “+” between the terms of one binomial and a “-” between the other (doesn’t matter which order) and the original binomial is factored! i.e. \((5x + 6)(5x-6)\)
Here are some key points to keep in mind when factoring the difference in two perfect squares with lead coefficients other than 1:
- Both terms in the original binomial must be perfect squares. This includes coefficients as well as variables.
- The operation between the two terms must always be subtraction
- The difference of squares will always factor into two binomials
- Be sure to take the square root of both the coefficients and the variable in each term.
- The terms in both factored binomials will be the same
- The only difference in the two factored binomials will be the signs. One sign will be “+” and the other will be “-“.
- It does not matter which binomial gets the positive sign and which one gets the negative sign.
- Answers can always be checked by applying the rules to multiply together two binomials using the factors to be sure you get the original binomial.
Video Highlights
- 00:00 \(5x^2-36\) single example of factoring a binomial perfect square with a lead coefficient other than 1
To watch this video on YouTube in a new window with clickable highlights, click here