Math 10 Week # 8

Beginning Week 8 of Math 10, the subject that we are moving on to is on Polynomials. These are expressions of two or more algebraic terms and we are leaning how to solve them. Before I begin with the examples, there are two key phrases we need to know, the first being like terms. Like Terms are two mathematical terms that share the same variable and exponent number (ie. 3 and 5). This is an important phrase to know because when we add or subtract polynomial terms, they have to be the same or like. The second phrase that we need to know is called Zero Pairs and this is when negative and positive numbers are added together, cancelling each other out. For example, If you add +5 and -7 together, there will be 5 zero pairs because there are 5 negatives and 5 positives cancelling each other out leaving a remaining -2. Think of it like Tug of War and the negatives and positives are on opposite sides. If there are 5 positives and 7 negatives, 5 of the negatives will balance out 5 of the positives but the negatives will win because they have 2 more on their side.

There are 4 different times of polynomials, them being Monomial (1 term), Binomial (2 terms), Trinomial (4 terms), and Polynomial (4 or more terms). For these examples, I will show you 3 different ways on how to multiply binomial terms together. The first way is to use an area diagram. This is a diagram where you separate the number in the terms we are using and multiply them when they intersect, like a punnet square. To start off, we are going to use multiply (2a + 5) and (a + 4) together; (2a +5)(a + 4). So what we do is we multiply the numbers that intersect each other and put the product in the boxes where the numbers overlap; (2a • a), (2a • 4), (5 • a), (5 • 4). Next we write out the numbers in an equation where different terms are separated and we add like terms together. In this case, we are adding 8a and 5a to make 13a and our final answer that’s simplified is 2 + 13a + 20.

The second way to find the product of a polynomial equation is using distributive property. This is when we split the numbers of the first term up and we multiply them to the second term individually, where we add them back together after. So for these next two examples, we are again going to use (2a +5)(a + 4). So what we are going to do is separate 2a and 5 and then multiply them separately with the second term; 2a(a + 4) + 5(a + 4). Once this is finished, we again add together its like terms and we again end of with 2 + 13a + 20.

Lastly, the third way to find the product of a polynomial equation is using a process called FOIL or The Claw. This process is very similar to distributive property and it is more focused towards visual learners. So FOIL is a term that stands for multiplying the First numbers of the two terms together, the Outside numbers together, the Inside numbers together, and the Last numbers together. The claw is a way of illustrating this process in a simple and easy way. So to begin, we multiply the first numbers (2a)(a), the outside numbers (2a)(4), the inside numbers(5)(a), and the last numbers (5)(4). Once this is done, we see that we are once again in a similar situation and we add like terms together and we end off with 2 + 13a + 20.

To conclude, these are three very easy ways to determine the product of binomials and each way will be good for different people. However, if you want to verify your answer and to check if you made any mistakes, this can be a way of checking your answer.