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EVILNess asks Algebra (HELP)
I suck at math. Specifically algebra.
Well, I am taking an online algebra class (Not cause I want to, trust me) and I am having a bit of a problem understanding an example. I would ask the teacher, but he never answers his goddamn email and I need some help now. It's been 9 years since I have done Algebra, and I don't remember a lot of the stuff it is assuming I know. (Don't worry, I am not asking you to do the problems for. Even if I want to.) I think I got everything right up to the point of "simplify." Which sucks because they just kinda jump on me like so: "Now you have: f(x) = 4(x-2)^2-2 NOW SIMPLIFY INTO f(x) = 4x^2-16x+14 CONGRATS ON YOUR ANSWER" How did they turn the first into the second? This sucks because I know I did this back in high school, but its been almost 10 years and yeah no matter how it nags the back of my mind I CAN'T REMEMBER. I don't even remember the name of what they are doing there to look it up! HELP. |
Just write it out fully, gather terms and such.
Firstly, take that squared on the bracket and apply it (squaring the bracket means you get two of them multipled) So you get 4(x-2)(x-2)-2 Expand the brackets (multiply left term with left term, left term with right term, right term with left term, right term with right term) 4(x^2-2x-2x+4)-2 Multiply the bracket with 4= 4x^2-8x-8x+16-2 Now just gather everything by how many orders of x they have (2, 1 or 0)= 4x^2-16x+14 There are faster ways to do it but pays do it step by step first. |
This stuff was always fun to me.
The order of operations/precedence is usually PEMDAS (parenthesis, exponents/roots, multiplication, division, addition, subtraction).
So, let's get from point A to point B. NOTE: I am using "X" for the variable and "x" for multiplication. f(x) = 4(X-2)^2-2 Our parenthesis contain the variable, so we'll move on to E and handle the exponent. In this case, we are squaring the (x-2). f(x) = 4(X-2)(X-2)-2 --or-- f(x) = 4 x (X-2) x (X-2) - 2 Continuing that bit, we multiply the pair: (X-2)(X-2) = X^2 - 2X - 2X + 4 = X^2 - 4X + 4 so f(x) = 4(X^2-4X+4)-2 Multiply again: f(x) = 4x(X^2) - 4x(4X) + 4x(4) - 2 f(x) = 4X^2-16X+16-2 Handle the integers and you get the final/simplified result: f(x) = 4x^2-16x+14 In this example, it's pretty straightforward, but make sure to arrange by order of the variable (X^n first, followed by X^(n-1) ... X^2 then X then integers/any number without a variable; of course it's more complex with polynomials that have multiple variables). |
Thank you, I think I got it now. Maybe.
We'll see. |
I still crack a smile at it.
If not, you could always go with your signature as an answer. That would certainly catch your teacher off guard.
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I would but it's all html forms for the answers.
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Pssh pemdas. It's BEDMAS or go home sucker.
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That just seems a little backwards to me.
B for "brackets"?
And you actually do division before multiplication? |
B is for brackets
Noes I do multiplication at the same time as division. You know, the way that it is supposed to be done. Also if anybody following and using the rules, addition and subtraction are done at the same time as well. |
Sheesh, how embarrassing.
Liike, I'm with you on that. You don't have to believe me, but last night I was not posting with my whole brain and apparently ignoring things I know. On another forum, I made a comment about a character in a comic not being present when he was clearly standing right there.
I just made myself to do some order-of-operations exercises as punishment. |
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