algebra factoring question, but SAT level (College Board official SAT practice exam)

The SAT math way of asking you a factoring problem! We are given a^2+b^2=z and ab=y, we have to find out 4z+8y and we will also have to factor this expression.

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#math #algebra #mathbasics

[scurfle]

I added the equations to get:
a^2 + 2ab + b^2 = z + 2y
(a+b)^2 = z + 2y
4(a+b)^2 = 4z + 8y
= 2^2(a+b)^2
= (2a+2b)^2

[dextr_coin]

Lol i find it weird watching this guy make high level calculus videos, and then make these basic algebra ones. It’s kinda weird.

[nousz]

I just did

4z + 8y
4(z + 2y)
4(a² + b² + 2ab)
4(a + b)²
(2a + 2b)²

[JavSusLar]

Yesterday I started imagining what would happen if I plugged atan(x) into sin(x): the interval (-π/2, π/2) would get infinitely stretched into a sigmoid. I plugged y=sin(atan(x)) into Wolframalpha and, to my surprise, it gave an exact equivalent function: y=x/√(x²+1) :oO Could you please explain WHY???

[jeeaspirant]

thumbnail seemed interesting and question was quite straight forward thanks for video

[Sgth]

Answer should be B. I ended up with 4(a + b)^2 but there were no choices with that so had to redo it.

[حسينالقطري-بص]

In the worst case, put a=b=1, which implies that
z=2
and
y=1
and
4z+8y=16

Option A: (1+2)^2 = 3^2 = 9 ≠ 16
Option B: (2+2)^2 = 4^2 = 16
Option C: (4+4)^2 = 8^2 = 64 ≠ 16
Option D: (4+8)^2 = 12^2 = 144 ≠ 16

Option B is the only true option. In case we have another option rerurn the value 16, then we need to have another substitution for a and b.

Claim: many SAT problems do not need formulae per say, can be done with trying the options, I am not discouraging you to learn formulae, but encouraging you to use "substitute and try" method in case you stuck.

Thanks for the video.

[lakjshashhsbd]

So do you just completely forget about the 8ab? Thats the only part i got lost. Not sure if they cancel out because they multiplied but uh yeah.

[ChunkyNosher]

Hello, I have a pretty interesting math situation, so if you see this, do you think you could make a video on it?

My sister who's in 3rd grade had a math test which was just normal multiplication, but then one of the questions in the test goes like this:

"Mr. Gomez had 87 stickers. He gave all of the stickers to his class of 20 students. Some students received 4 stickers and the others received 5 stickers. How many students received 5 stickers?"

I haven't practiced any high-school level algebra or calculus since I'm a freshman undergrad in college with a non-stem major, so I'm pretty washed with my math skills, but doesn't this problem require a system of equations, which is high school level math? Is there any reasonable way that a 3rd grader could get the correct answer without a system of equations or trial and error?

I also emailed you with further details including the image of the problem with both my own work and my sister's work. This issue has been weighing in the back of my head for a while now, so I'd be grateful if you were able to solve this and give me peace of mind.

[shohomchakraborty]

Well I mean the 4z itself is already just 4(a^2+b^2) or 4a^2+4b^2. The square root of 4a^2 is 2a, so the only answer choice it actually could be is choice B. Too easy

[PhilosophicalNonsense-wygy]

Bro that way is just too much hard work i did it easier way

[Proferk]

Why do all that tic tac toe nonsense when you can just factor it using the (a+b)^2 identity?