For, the like terms will cancel. (Lesson ) Symmetrically, the difference of two squares can be factored: x2 − 25 = (x + 5)(x − 5). x2 is the square of x. 25 is the. Intermediate Algebra Skill. Factoring the Difference of Squares. Factor each completely. 1) 9x. 2 − 1. 2) 4n. 2 − 3) 36k. 2 − 1. 4) p. 2 − 5) 2x. 2 − Here are some examples showing the range of expressions that qualify as a difference of squares. Example: Factor x 2 − 4. The second term can be thought of.

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A sum of squares cannot be factored over the real numbers but over the complex numbers it can be factored like this: You can easily verify this by multiplying out the right hand side and then canceling the cross terms: Other Stuff Try to Factor a Polynomial by Rewriting It as the Difference Between Two Squares Factoring a difference of squares you are working on "factoring a polynomial," sometimes your polynomial can be written using the difference between two squares.

The a term from the difference of squares problem must be placed where the a term appears in the answer.

- - Difference of Squares
- Factoring Polynomials: The difference of two squares
- 2. Common Factor and Difference of Squares
- 2. Common Factor and Difference of Squares
- How Do You Factor a Polynomial Using Difference of Squares?
- Factoring Difference of Two Squares

The same applies for the b terms. Let's take a look at a couple more examples. Example 1 Factor the expression x2 - 16 First, let's see if this is, in fact, a difference of factoring a difference of squares problem. There are definitely two terms with a minus sign between them, but is each term a perfect square?

This meets the criteria for the pattern, so we can factor it using the pattern.

Just bring down the 3 in factoring a difference of squares of the parenthesis. We can check this by multiplying everything out. Begin the factoring process by writing two sets of open parentheses: Now find the square root of 4x2, the first term, by finding the square root of 4 and then dividing each exponent by 2.

The square root of 4 is 2. Half of the exponent 2 is 1, thus x2 becomes x1 or x.

## Difference of squares | Factoring quadratics (article) | Khan Academy

Thus, the square root of the entire term is 2x. Write this term on the left inside of each set of parentheses. In this case they can not so the final answer is: Example 2 — Factor: