I learned last week how to multiply two binomials using area models, this week I learned how to multiply a binomial with a trinomial using area models

As you can see it is the same concept as using area models for 2 binomials but instead of it being a square we make a triangle because it has one side that is 3 squares long for our trinomial and 2 squares for out binomial. Once we have our numbers on the side of it, we multiply the numbers on the outside of the box and we should come out with 6 numbers and then we can combine the like terms like it shows the underlined numbers, once we combine the numbers we have out answer.

One Thing I learned this week was how to multiply binomials using area models which is basically simplifying it using 4 boxes, for example.

as you see we use the 4 boxes, we first put the numbers on the side and we multiply the number that are outside the box and put the answer in the box in between them. on the top of the box I wrote which number are being multiplied.

after you have all your numbers in the boxes, make sure you combine all the like terms, for example I underlined 35x and 8x because they are like terms that can be added together, In the end you should end up with your answer, the answer I got for my question is 14² + 43x + 20.

One thing I learned this week was finding angles in a right triangle.

The first step to finding the angle is to first distinguish what ratio we are going to use by narrowing it down by using “SOHCAHTOA” and we can see that the Adjacent side doesn’t have a unit on its side so we take off the ratios that use adjacent which removes Cosine and Tangent, leaving us with a Sine ratio. Then, we put it into an equation.

The second step is solving. once we have our equation, the first thing we need to do is isolate the variable which is that zero with a line through it also known as theta. So, in order to isolate the variable, we move the Sine to the other side of the equal sign which turns it negative, also called an “Inverse Sine”. once we put this on our calculator, we should get the answer 33.1 if we rounding to nearest tenths, but if we are rounding to nears whole number then we will be left with 33 and make sure you put a degree sign on you answer so we would have an answer of 33°.

One thing I learned was how to distinguish the different ratios using the acronym “SOHCAHTOA”.

the acronym stands for “sin opposite hypotenuse, cosine adjacent hypotenuse, tangent opposite adjacent”.

you can implement it in a question like this for example, you can see that the side are labeled and we units on the hypotenuse side and the adjacent side, but we don’t have anything on the opposite side so we know the ration cant include an opposite side on it. when we look at “SOHCAHTOA” to see which ratio we will be using, we can take off the ratios that have an opposite side in it so, that removes both Sin and Tangent, which leaves us with Cosine to finish our question with.

One thing I improved on this week was finding the LCM in two numbers. I improved because in grade 9 I feel that I wasn’t the best at finding the LCM but now I feel that with the ways I learned this week, I feel that I can do it much easier.

A time I used math this summer was when I was home playing on my PlayStation 5, and I wanted to purchase a monthly subscription to PS plus, which lets me play games online and also gives me some free games. Since I am pretty broke, I had to calculate how many months I can pay for it before I become poor. The monthly price for PS plus is $12 per month so I could get around 3 months of it before I’m officially poor.