__Factoring Formulas__:

- (a + b)
2 = a
2 + 2ab + b
2 Square of a Sum
- (a − b)
2 = a
2 − 2ab + b
2 Square of a Difference
- a
2 − b
2 = (a − b)(a + b) Difference of Squares
- a
3 − b
3 = (a − b)(a
2 + ab + b
2
) Difference of Cubes
- a
3 + b
3 = (a + b)(a
2 − ab + b
2
) Sum of Cubes

__Factoring Calculator__:

##### What is it? - Finding what was multiplied together (“the factors”) to get an expression (the
polynomial).

##### Why is it done? – To aid in solving equations.

##### How is it done? – Follow the general steps outlined below in order.

#### How to factor expressions

###### If you are factoring a quadratic like 1x^2+2x+1 you want to find two numbers that

- Add up to 2
- Multiply together to get 1

###### Since 1 and 2 add up to 2 and multiply together to get 1, we can factor it like: (x+1)(x+2)

### What is factoring?

Well, factoring is the process of finding what to multiply together to get an expression. So let's take a look at an example of a polynomial in its expanded form as well as its factored form. If you take the polynomial form of X^2+7X+12 and you ask yourself the question what do I have to multiply together to get that expression? You're asking to find the factored form of that polynomial. And the factored form of X^2+7X+12 happens to be (X+3) times (X+4) Now you might recognize this from a previous chapter on distribution and multiplying polynomials. So, to check and just make sure that this truly is the factored form of this polynomial you would simply multiply it back out using distribution. So we'll distribute the X to each term in the second polynomial and then I'll come back and distribute the 3 to both terms of the second polynomial. When you multiply X times X, you get X^2 and X times 4 is simply positive 4X. Coming back and multiplying the 3 by X, I get positive 3X and multiplying the 3 by the 4 I get positive 12. Now you also learned in a previous chapter that you should always combine like terms and when we do so we end up with the polynomial X^2+7x+12 which is exactly what we began with in our polynomial form. So the factored form of this particular polynomial is (X+3) times (X+4).