Multiplying Polynomials

This week in math class I have learned how to FOIL when multiplying polynomials as well as using an area diagram.

FOIL is a distributive technique when multiplying polynomials together.

F: First term in each bracket  (a+b)(c+d)   first term: $a \cdot c$

O: outside terms        (a+b)(c+d)    Outside term: $a \cdot d$

I: inside terms        (a+b)(c+d)     Inside term: $b \cdot c$

L: last term in each bracket        (a+b)(c+d)   Last term: $b \cdot d$

example: ( $a^2+8$)( $a^2-8$)

F: First term in each bracket

You are taking $a^2$ and multiplying it with the other $a^2$ in the other bracket which will then give you $a^4$ because you add the exponents when the bases are the same during multiplication.

I: Inside terms

You have to make  sure to multiply the first term with the other term as well, everything that’s inside the other bracket, so in this case, $a^2$ will be multiplied with (-8) which will be $-8a^2$.

You are now left with $a^4-8a^2$.

O: Outside terms

You have multiplied the first term with everything in the other bracket and the inside term with the other term, you now need to do the same for the outside term. In this case, you now need to multiply 8 with $a^2$ which will give you $8a^2$. $(8)(a^2)=8a^2$

L: Last terms

Then you multiply 8 with the second term in the other bracket.

8(-8) = -64

Now put all the terms together in descending order by the exponents and collect like terms if needed. $a^4-8a^2+8a^2-64$ $-8a^2$ and $+8a^2$ cancel out so you are now left with : $a^4-64$

This is Foiling but I learned a quicker technique that you can use depending on each equation.

Example: $(x+7)^2$

Instead of expanding the equation then simplifying, you just need to square x = $x^2$, then multiply x with +7 and double it = $7x \cdot 2$ = 14x, then square the last digit which is 7 = $7^2$ = 49. Now you are left with: = $x^2+14x+49$

The hardest part of this lesson was when I had to find the area of a rectangle/square when it had empty areas, so you had to find out the angles by subtracting then multiplying and other steps which was a little confusing. But I will keep practicing these equations.

Surface Area and Volume

This week of math class, I’ve learned how to find the volume and the surface area of prisms, cones, pyramids and spheres, as well as learned some new formulas that I can use. Right here  I am looking for the volume and surface area of a prism. In this example, I needed to use Pythagorean Theorem because the height length was not given to find the area of the triangular base.The idea of Surface Area for prisms is to add all the areas of the surfaces/faces.

The most challenging part about learning this lesson was finding the Surface Area because it requires a lot of steps and you can accidentally make a small mistake which changes the answer completely.

Imperial and SI systems

This week we learned  quite a few things I’ve learned from Imperial and SI systems. I’ve learned more different conversions in measurements such as converting from feet to miles and meters to yards. I’ve also learned how to read a vernier caliper in Imperial and metric units and how to read a micrometer in metric units.When you are given multiple measurements, sometimes you have to do multiple conversions because some of the conversions are not given.

For example meters to feet. You have to go through multiple conversions, meters to centimeters then to feet.

For example 16m to feet = 52 inches

What I learned this week

This week I learned how to calculate an angle using trig functions such as sin,cos, and tan.

What I learned in Math

I learned how to solve negative exponents by turning them into positive exponents and then solving them while using the exponent laws

LCM/GCF

Here is a 2nd method to find LCM. That I used in kumon. List the multiples of both numbers until you see a common one.

For example: 150 and 10

1*150=150                              15*10=150

So the LCM is 150

Here is a 2nd method to find the GCF:

List all the factors until the both numbers have the same factor.

For example 104 and 320

Factors of 104                                                                Factors of 320

1,2,4,8,13,26,52,104,                                                    1,2,4,5,8,10,16,20,32,40,64,80,160,320,

The GCF of 104 and 320 is 8.

Personally I prefer the prime factorization method then these two,because it will take a long time to do these two methods with big numbers.