There are 3 patterns that can be found in polynomials:

1. Multiply 2 Binomials

First term = multiply both terms together – 

second term = sum of last two terms together – 7x

 

third term = multiply both terms together – 12

this saves you time from double distributing and allows you to solve it quicker.

2. Multiplying Conjugates

Ex. (x-2)(x+2)

 

Here is algebra tiles to show you how it works.

We can multiply the first term and last term to get the answer.

If you look at the algebra tiles, the negative x and positive x cancels each other out and you are left with  – 4

3. Perfect Square

If there is a question like -25, it would be easy to solve as we know that since 25 is a perfect square we can find the square root, which is 5, and multiply it twice because we are just splitting the numbers. Therefore, (x-5)(x+5) is the factored form of -25 by using perfect squares.