Factoring a Difference of Two Squares
Step 1.* Ask yourself if the problem can be undistributed.
Step 2. Ask yourself if the given expression is a difference of two squares.
Step 3. If so, set up two sets of parentheses that resemble the following.
Step 4. Square root the first term of the given expression to calculate the first term of each new binomial.
Step 5. Square root the second term of the given expression to calculate the second term of each new binomial.
* This is the first step of all factoring problems.
Directions: Please factor the following expression.
Step 1. The problem can not be undistributed. Nothing goes into 9 and 25 evenly.
Step 2.
| Does the given expression have two terms? | YES | |
| Is it a difference (subtraction)? | YES |
| Is the first term a perfect square? | YES | 9 is a perfect square and the
exponents are all even |
| Is the second term a perfect square? | YES | 25 is a perfect square |
Step 3.
| Step 4. | The
square  root of is  . |
When we square root a monomial, square root the coefficient and divide all the exponents by 2. |
| Step 5. | The square root of 25 is 5. | |
Directions: Please factor the following expressions.
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Directions: Please answer the following question.
21. What are the dimensions of a rectangle that has an area of 9x2-25?
Directions: Please write 1-2 paragraphs that thoroughly address the following.
1. Why does having all even exponents and a perfect square coefficient denote that a monomial is a perfect square? (Hint: Consider the fact that a perfect square is a number that when square rooted yields an integer.)
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