Notes

(x+3)(x-7) (6m-4)(8m+3) | we are learning alot today so take notes i recommend it
x2-4x-21 48m2-14m-12 | ~ms.lewis (aka: coolest kid in school)
_____________________________________|____________________________________________________
8.4 notes
multiplying special cases

the square of binomial "tricks"
(a+b)^2=(a+b)(a+b)=a^2+2ab+b^2
(a-b)^2=(a-b)(a-b)=a^2-2ab+b^2
example: (x+4)^2=x^2+2(1)(4)x+4^2
=x^2+8x+16

solve: (x+8)^2=(x+8)(x+8)=x^2+2(1)(8)x+8^2
=x^2+16x+64

(2m-3)^2=m for magic
=4m^2-12m+9
_________________________________________________________________________________________

we are gunna look at this example on math xl. so lets say this is like uh outdoor patio. lets say uh this is the fire pit. we gotta find out like this is the fire pit. this tiny square x-1 x-1. how do we find the shaden gree? so that tells us the area of the whole square, we wanna find out the area of the shaded area. lets say this is the largest square, minus the area of the smaller square. it looks like this a^2 plus b^2. now we could either [tin] foil or use the formula. remember is a^2 minus 2ab plus square.[*clicks computer].well i don understand when ur talking about this like this is the answer [and im right because im right] cus this is the answer. we are gunna find the area of the shaded region in terms of x. so heres my a and heres my b. plus b squared so thats plus 25. minus so we have a minus b squared. so we have x squared. minus 2x minus b square. how do we do that on the area of the smaller square. so we combine like terms so those go away. 10x-2x--[negative]2x=24we are gunna find out what a square is without a calculator [the struggle is real].how do we solve this problem no calculator just your brain.how can i make 39 look something like a plus b. well u would still have to do like 39 squared in your head. you could do 40-1. why would 40 - 1 be easy to do in our head [the struggle is real]? lets use 40-1. everyone okay with knowing 40-1 is the same as 39? [everyone says: NO]. in terms of a and b. plus b. so we have a squared minus 2 ab minus b squared whats 40 squared without using your calculator.1600, so we have a squared is 1200 [1600]. minus 80 plus b squared. so now we just have to simplify it. [*ben walks in].
21 yeah. so break down the pieces. so without using your calculator you found out what 39 squared is. it is really cool.so we have 85 squared. do it now. we have a - bsquared and a + bsquared...
_________________________________________________________________________________________

what is 85^2? i didn't use my calculator. #mentalmath
the answer is 7225

_________________________________________________________________________________________
... a is my five and five is my b. what is a squared? [64]! thats right, 2 zeros. 800 yus.plus five squared thats twentyfive. 6400 add another 200 now we are at 7200! the answer is 7225 [im smart]. do you guys wanna see the other way. [everyone says: no]. OKAY LETS DO IT! so i have 8100 as b squared. so that times five is about 800. so minus nine hundred and plus 25 you get seven hundred and twothousand! [everyone says: no]. [ms.lewis objects]. [the answer is 7225.]. okay this is our last slide [exactly 53025 slides later...]. so this is our last slide. so a squared minus b squared minus ab positive a plus positive b is plus ab equals zero. so you get a sqared minus b squared. [joe says: something stupid and inaudible.]. that is how you would [tin] foil it out!. x squared minus four! so i want you to try number four...
_________________________________________________________________________________________

(x^3+8)(x^3+8)=x^6+8x^3+8x^3+64 no calculator #smarticle #particles
=x^6+16x^3+64

_________________________________________________________________________________________
...k heres our last example. heres our challenge problem. use mental math to solve...put it in this format
solve 64*56 [everyone mentally says: is it that hard[
_________________________________________________________________________________________

64*56=3584

_________________________________________________________________________________________
...[everyone mentally says: that was hard]. guys i cant even hear myself think. whats the trick that we learned to solve this quick. why 60 times 60. not even [tin] foiling. whats the new trick besides [tin] foiling? a squared minus b squared. b is 4 so 4 squared. no 16. 3000500 - 16 its makin me nervous. whats 800 - 16. yeah ahundred minus 16 is 84 so [through the power of logic] the answer has to be 3564 [she mispronounced again....][][][][][][][][][][][][][][][][][][][][][][][][][][][][the answer is 3584][][][][][][][][][][][][][][][][][][][]
scott SCOTT. we get y or what ever minuscule. and we talkaboutda producl of a squared and v squared. [tin] foil still does work. we will have to do these methods later cus they are quicker. u think im dumb so im just gunna [tin] foil. friday is ur quiz. gud job wit da methods.

~ms.lewis (aka: most style-ish kid in school)

stay in school kids @a_turkey_walrus