Patterns can be found in polynomials using number equations or algebra tiles…..

1) Multiplying 2 Binomials-

If we have, ex. (x+2) (x+3) , we can find all 3 terms without doing double distributive:

-First term: multiply  the first 2 terms together, =                               -Middle term: the sum of the two last terms (including the x) = 5x         -Last term: multiply together the last 2 terms together, = +6

SO, our answer all together is….

2) Multiplying Conjugate-

If we demonsrate the conjugate (x +2) (x-2) with algebra tiles,

We can see that the answer is which shows that we can multiply the first term, and the last term to get the answer.

If we look closer at the picture, there are the SAME number of positive x’s and negative x’s. (The middle term cancels out!)

*Another interesting thing is that one portion of the model is white (negative) and the other portion is coloured in (positive) because the binomial is a conjugate.

3) “Perfect Square Questions”

ex. can be easily solved as (x+9) (x-9) if we understand that 81 is a perfect square number and can be split into 2 of the same numbers. (Positive and negative) This patter works for even more challenging questions that have all perfect square numbers.