For the past 2 weeks we have been learning all about polynomials, and when there are many terms or big equations that will take a whole to solve we don’t want to waste our time solving one question, so we use patterns to simplify the polynomial to solve it quicker!

The first type of pattern we learned was for multiplying polynomials.

For a binomial that has the same numbers in each term you multiply the first term in each bracket by each other to get the first term in the simplified equation. To get the middle term you multiply the numbers inside each bracket and add them together. To get the last single number you multiply the number in each term by each other. With this process you can easily simplify a polynomial equation with the same terms without half the work.

Ex.

The next pattern we learned was with conjugates, which means you have a binomial both with the same equation, but one being a subtraction, and one being an addition, and with this it creates a zero pair. You start off by multiplying the first number in each term together and then the last numbers in each term by each other. And because of the zero pair the 4 numbers multiplied is the answer.

Ex.

We also learned a pattern for simple binomials with X in the front. With these equations you can multiply the 2 X’s, which will be X squared, then add the 2 last numbers in the equation to get X. Then, to get the single/last number in the equation you multiply the 2 last numbers in the brackets. With this pattern you will always end up with a trinomial for an answer.

Ex.

 

For trinomials we also learned a few smaller patterns to help with finding the simplified equation such as:

• All the exponents on the first term can be halfed evenly.
• If the equation is not in order, you can order it.
• If the equation has a 3 as an exponent, it can still work.
• You can use double pattern.

Double Pattern Ex:

The last pattern we learned was with algebra tiles:

• If you have a + and a -, half of the squares will be shaded.
• If you have a + and +, everything will be shaded.
• If you have a – and -, the two corners will be shaded.