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Factoring binomials as difference of squares

A binomial is factorable only if it is one of three things a Difference of Squares, a Difference of Cubes, or a Sum of Cubes. A binomial is a Difference of Squares if both terms are perfect squares. Recall we may have to factor out a common factor first.

If we determine that a binomial is a difference of squares, we factor it into two binomials. The first being the square root of the first term minus the square root of the second term. The second being the square root of the first term plus the square root of the second term.

A binomial is an algebraic expression consisting of two terms. The difference of squares is a special case of factoring where a binomial can be factored into the product of two binomials.

The formula for factoring a binomial as the difference of squares is: $a^{2} - b^{2} = (a + b) (a - b)$ .

Step-by-Step Process

To factor a binomial as the difference of squares, follow these steps:

Identify the square of each term in the binomial.
Write the binomial as the difference of squares using the formula above.
Factor the expression if possible.

Example

Let's factor the binomial $x^{2} - 9$ as the difference of squares:

Step 1: Identify the squares - $x^{2}$ and $9$ are both perfect squares.

Step 2: Write the difference of squares - $x^{2} - 9 = (x + 3) (x - 3)$ .

Step 3: The expression is now factored as the difference of squares.

Factoring binomials as the difference of squares is a fundamental technique in algebra and is often used in various mathematical problems.

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Factoring binomials as difference of squares

Step-by-Step Process

Example

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