Trouble understanding why two equations give the same result

[Sam Scott]

Hello,

I feel like I should know this already and feel foolish having to ask, however can someone please explain why:

$$a^2 - \frac {b^2a^2} {c^2} = d$$ is the same as: $$a^2 (1 - \frac {b^2} {c^2}) = d$$

Again, sorry if this really is something incredibly obvious, for some reason I am just blanking. All I need to know is what I need to look up to understand

Thank you in advance and this is my first post so I am sorry if this is in the wrong area or anything like that,

Sam

 

[Bystander]

Reread what you've been taught/learned about the "distributive law."

 

[Sam Scott]

Thank you for replying, I'm re-reading what I have on the distributive law but I can't see how to apply that to the equation, I'm sorry about this, I've been looking around for a long time by myself not wanting to waste anybody's time and now when somebody is telling me what to look at I'm still not seeing it.

 

[Bystander]

What's "a² x 1 ?" What's "a² x b²/c² ?"

 

[Sam Scott]

So in summary yes I was being an idiot. Truly have no idea why this has caused me a problem, but thank you very much for your help!

Very glad I've found this site as something like this is bound to happen to me at some point (for example in the next hour maybe?)

Sam

 

[epenguin]

If we call b²/c² x, would it be obvious that a² - a²x is the same as a²(1 - x) ?.

In general when sonething appears in every term of an expression it is a factor of that expression.

 

[Sam Scott]

That also helps, thank you as well! Hopefully I've replied quickly enough to stay out of your black book

 

[Mark44]

Since this isn't really a homework problem (that I can see), I have moved it.

 

[Mentallic]

Keep in mind that

$$a^2\times \frac{b^2}{c^2}=a^2\frac{b^2}{c^2}=\frac{a^2b^2}{c^2}=\frac{b^2a^2}{c^2}$$