Before looking at some factoring expressions examples, it helps to be clear about what exactly a factor is in Math.

Firstly, we can recap what a factor is when we are dealing with numbers.

### Factors with Numbers:

A factor of a certain number, is any other number that exactly divides the certain number, leaving no remainder.

This includes the certain number itself.

We could have the number

**16**.

The factors of

**16**are:

**1**,

**2**,

**4**,

**8**and

**16**.

\bf{\frac{16}{1}} \space = \space 16 , \bf{\frac{16}{2}} \space = \space 8 , \bf{\frac{16}{4}} \space = \space 4 , \bf{\frac{16}{8}} \space = \space 2 , \bf{\frac{16}{16}} \space = \space 1

So we can multiply some factors together to get the original number, such as

**2**×

**8**=

**16**.

This same logic and process also applies to expressions as well as numbers.

### Factors with Expressions:

Similar to numbers, when dealing with factoring expressions examples we are looking to separate an expression into factors that can be multiplied together.With the expression 2x+6, we can factor.

What we want to do, is look for a common factor that both terms share, if we recall the distributive property,

a(b+c) \space = \space ab+ac.

2x+6 has a common factor of 2, so we can factor as follows.

2x + 6 \space = \space 2(x + 3)

The factors of 2x+6 are 2 and (x+3).

## Factoring Binomials Examples

A binomial is an expression in Math that contains two terms.

*(1.1)*Factor 2a^2 + 8a^3.

*Solution*2a^2 is a common factor of both terms.

2a^2 + 8a^3 \space = \space 2a^2(1 + 4a)

*(1.2)*Factor x^4 – 36.

*Solution*We can look to put both terms into square form.

x^4 – 36 \space = \space (x^2)^2 – 6^2

Now from here we can recall the difference of two squares property.

(x^2)^2 – 6^2 \space = \space (x^2 + 6)(x^2 – 6)

We can actually factor a little bit further here, with (x^2 – 6).

(x^2 + 6)(x^2 – 6) \space = \space (x^2 + 6)(x – 6)(x + 6)

*(1.3)*Factor 25c^2d^4 – 4e^2.

*Solution*25c^2d^4 – 4e^2 \space = \space (5cd^2)^2 – (2e)^2

= \space (5cd^2 – 2e)(5cd^2 + 2e)

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