Factoring Difference of Squares #1
Description/Explanation/Highlights
Video Description
In this video the method for factoring the difference of two perfect squares is explained.
Steps and Key Points to Remember
To factor the difference of two perfect squares, follow these steps:
- Before starting, make sure both terms are perfect squares. In the example \(x^2-49\) both terms of the expression are perfect squares. i.e. \(x^2 = x \cdot x\) and \(49 = 7 \cdot 7\)
- Also, make sure the operation is subtractions. 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 \(\sqrt{x^2}=x\)
- x is the first term of each binomial
i.e. (x )(x ) - Repeat the process and find the square root of the second term. In our example \(\)\sqrt{49}=7
- 7 is the second term of each binomial
i.e. (x 7)(x 7) - 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. (x + 7)(x – 7)
Here are some key points to keep in mind when factoring the difference in two perfect squares:
- Both terms in the original binomial must be perfect squares.
- The operation between the two terms must always be subtraction
- The difference of squares will always factor into two binomials
- 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 \(x^2-49\) single example of factoring a binomial perfect square with a lead coefficient of 1
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