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Factoring Expressions in Algebra,
Factoring Binomials Examples


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)



(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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