Help with basic algebra question

So I've been out of school for quiet a few years. I've forgotten a lot of what I've learned about algebra but I've been studying trying to pick it back up. I have a test coming up for a job that I've applied for. It's not just the test though. I've struggled with math for most of my life and I'm ready to start studying every day so it can just stop being a barrier for me. I would consider myself a fairly intelligent person but something about my brain and numbers has just never mixed and I want to change that.

I have a sample question sheet for my upcoming test. If this sheet were the full test I would have it aced with the exception of one question:

Quote:

Consider the following formula:

7=3(x+5)(x-2)

Which of the following formulas is equivalent to this one?

A. y=3x^2 + 9x - 30

B. y=x^2 + 3x - 10

C. y=3x^2 + 3x -10

D. y=3x^2 + 3x - 30

Now this is clearly going to be a pretty basic question for a lot of you so don't go too hard on me. I understand how to simplify some easier equations, but something about this one is confusing me. (Headbang)

Can someone explain which one is equivalent and why? Thanks

Re: Help with basic algebra question

What? I'm not allowed to be hard on you? No fun!

It's not what we would normally call simplifying but just "multiplying". Using the "distributive law" we multiply each part of (x+ 5) by (x- 2) we have $\displaystyle x(x- 2)+ 5(x- 2)= (x^2- 2x)+ (5x- 10)= x^2+ 3x- 10$. Finally, multiply each part of that by 3: $\displaystyle 3(x+ 5)(x- 2)= 3x^2+ 9x- 30.$

Re: Help with basic algebra question

Ok. I understand what you did there! I think I misunderstood how to correctly apply the distributive law to multiple sets of parentheses and that's why I couldn't get to any of the listed answers. I'm definitely going to need to study this more.

Thank you my good sir :D