So far we’ve learned three factoring techniques. The first one, **common factoring**, is a technique that can be used for any polynomial. The other two were specific for quadratics, namely **trial-and-error** and **decomposition**.

The whole purpose behind factoring any quadratic – if you haven’t discovered already – is convert it in such a format that enables you to solve for the x intercepts (the roots). A whole unit will be dedicated to solving equations, including first and second degree equation. Otherwise, if it’s in **general form**, you can’t easily do that.

You’ll find out here that some quadratics whose **b-term** is missing and whose **a** and **c terms** are being subtracted, can be factored by another technique known the **difference of squares**. Examples of quadratics that fit this pattern look like this:

- y = x² – 100
*(easy)* - y = 98a² – 450b²
*(medium)* - y = (3x + 8)² – (x – 2)²
*(hard)*

Also, as the name of the technique implies, both terms in the quadratic need to be **perfect squares** (*squarootable*).

Take equation (1) as an example. Taking the **square root** of x² yields x. In other words, √x² = x. Similarly, √100 = 10. In the second equation, after common factoring **2** from both terms, you get:

= **2**(49a² – 225b²)

Notice now that √49a² = **7a** and √225b² = **15b**. Both terms within the parentheses are perfect squares; hence, this technique can be used.

In equation (3), the square root of (3x + 8)² is **3x + 8** and the square root of (x – 2)² is **x – 2**; therefore it fits the same mold. A summary of what’s required is written below.

Conditions required to factor a difference of squares:

- b term needs to be missing.
- The two remaining terms are being subtracted.
- The two remaining terms need to be a perfect square.

Let’s what a few examples: