1. Help Finding equivalent expression

Hi guys, this is my first post here, but I have a feeling I will be back pretty often as I am completely lost when it comes to math. Right now I am just studying before I even take my placement test for college, because I don't necessarily want to be completely clueless even for a placement test.

Anyway:

tē- 59t + 54 - 82tē + 60t is equivalent to:

I am really lost. I know that getting the answer to this problem has something to do with order of operations but if someone could teach me the correct way to go about solving this problem I would REALLY appreciate it. I have an entire sheet that I got off the internet which is a college entrance exam practice test, so that is where I am getting these problems.

2. Originally Posted by KimuraJoe

Anyway:

tē- 59t + 54 - 82tē + 60t is equivalent to:
Grouping like terms

$-81t^2+t+54$

3. combine like terms

looks like they want you to just combine like terms

4. it can be factorized....but the two solutions for x look terrible

5. Originally Posted by ukorov
it can be factorized....but the two solutions for x look terrible
what do the solutions for t look like?

6. Originally Posted by pickslides
what do the solutions for t look like?
$- \frac{1 \pm \sqrt{17497}}{162}$

7. Yeah, thanks, I have the answer here in my answer key I was more interested in the process. Like I said, it's been a very long time and when I googled on how to do it this is what I found; Equivalent expressions

That guy just uses alot of terminology I don't understand and I was hoping one of you guys could explain it a little better for someone that isn't experienced with mathematics at all. I haven't taken a math class in over 3 years and when I was in a math class I wasn't really interested in learning so now I'm paying for it.

8. Originally Posted by KimuraJoe
Hi guys, this is my first post here, but I have a feeling I will be back pretty often as I am completely lost when it comes to math. Right now I am just studying before I even take my placement test for college, because I don't necessarily want to be completely clueless even for a placement test.

Anyway:

tē- 59t + 54 - 82tē + 60t is equivalent to:

I am really lost. I know that getting the answer to this problem has something to do with order of operations but if someone could teach me the correct way to go about solving this problem I would REALLY appreciate it. I have an entire sheet that I got off the internet which is a college entrance exam practice test, so that is where I am getting these problems.

It has to do with "combining like powers". For example, $t^2- 82t^2= (1- 82)t^2= -81t^2$.

9. Originally Posted by HallsofIvy
It has to do with "combining like powers". For example, $t^2- 82t^2= (1- 82)t^2= -81t^2$.
Sorry like I said, I'm essentially brand new at this. Where does that 1 come from? When I looked at the answer that's one of the main things I did not understand, is how you get $81t^2$ from $t^2-82t^2$ do you just assume that t = 1 ?

10. Originally Posted by KimuraJoe
Sorry like I said, I'm essentially brand new at this. Where does that 1 come from? When I looked at the answer that's one of the main things I did not understand, is how you get $81t^2$ from $t^2-82t^2$ do you just assume that t = 1 ?
Do you know how to simplify a - 82a?

11. $1$ is the coefficient of $t^2$ as $1\times t^2 = t^2$

You should check out Practical Algebra Lessons it explains the basics really well in my opinion.

12. Originally Posted by KimuraJoe
Sorry like I said, I'm essentially brand new at this. Where does that 1 come from? When I looked at the answer that's one of the main things I did not understand, is how you get $81t^2$ from $t^2-82t^2$ do you just assume that t = 1 ?
You need to make sure you are comfortable with distributivity, it is a fundamental property of algebra. It states, in simple terms:

$yx + zx= x(y + z)$

Let's look at a simple problem and apply the rule. All I have done is stated the above, where y = 2 and z = 3a:

$2x + 3ax = x(2 + 3a)$

Now, if you get this, then consider the following:

$x+3x^2=x(1+3x)$

Once again, all we've done is set y=1 and z=3x. So we just multiply the x outside the brackets with each term inside the brackets: $x \cdot 1 = x$, and $x \cdot 3x = 3x^2$

I would really make sure you understand three rules before attempting any of these problems:

Commutativity
Associativity
Distributivity

We basically use these three rules to solve most types of algebraic problems.