Trouble understanding why two equations give the same result

  • Thread starter Sam Scott
  • Start date
In summary, the equation a^2 - \frac {b^2a^2} {c^2} = d is the same as a^2 (1 - \frac {b^2} {c^2}) = d. This is due to the distributive law, which states that when multiplying a number by a sum, you can distribute the multiplication to each individual term within the parentheses. In this case, we can rewrite \frac{b^2a^2}{c^2} as a^2 \times \frac{b^2}{c^2} and then apply the distributive law to get a^2 - a^2\times \frac{b^2}{c^2
  • #1
Sam Scott
4
1
Hello,

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

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

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
 
Mathematics news on Phys.org
  • #2
Reread what you've been taught/learned about the "distributive law."
 
  • #3
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.
 
  • #4
What's "a2 x 1 ?" What's "a2 x b2/c2 ?"
 
  • Like
Likes Sam Scott
  • #5
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
 
  • #6
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.
 
  • Like
Likes Sam Scott
  • #7
That also helps, thank you as well! Hopefully I've replied quickly enough to stay out of your black book
 
  • Like
Likes epenguin
  • #8
Since this isn't really a homework problem (that I can see), I have moved it.
 
  • #9
Keep in mind that

[tex]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}[/tex]
 

FAQ: Trouble understanding why two equations give the same result

1. Why do two equations give the same result?

Two equations can give the same result because they are mathematically equivalent. This means that they express the same relationship between variables, just in different forms. For example, the equations y = 2x and 4y = 8x both represent a linear relationship between y and x with a slope of 2.

2. How can I tell if two equations are equivalent?

You can tell if two equations are equivalent by simplifying each equation and comparing them. If they have the same variables, coefficients, and constants, then they are equivalent. Another way to determine equivalence is by graphing the equations and seeing if they produce the same line.

3. Can two equations that look different still be equivalent?

Yes, two equations that look different can still be equivalent. For example, the equations 3x + 2y = 12 and 6x + 4y = 24 are equivalent. The second equation is just a simplified version of the first equation, with both sides divided by 2.

4. Why is it important to understand equivalent equations?

Understanding equivalent equations is important because it allows us to manipulate and solve equations in different ways. For example, we can use equivalent equations to isolate a specific variable or to solve for a system of equations. It also helps us understand the relationship between different forms of equations.

5. How can I use equivalent equations to solve a problem?

You can use equivalent equations to solve a problem by manipulating the given equations to get them into a form that is easier to work with. For example, you can use the distributive property to simplify equations, or you can combine like terms to eliminate variables. By creating equivalent equations, you can simplify complex problems and make them more manageable to solve.

Similar threads

I Are there any two pairs of integers with the same result in a specific function?
Replies
7
Views
1K
A Are these two optimization problems equivalent?
Replies
1
Views
1K
I Trouble Solving an Equation that has square roots on both sides
Replies
1
Views
1K
Why is 1 not equal to 0 in this proof?
2
Replies
66
Views
4K
B Understanding the relationship between ratios and fractions
Replies
8
Views
513
B Understanding why πr^2 works for different area calculations
Replies
7
Views
645
A Help needed with derivation: solving a complex double integral
Replies
1
Views
1K
MHB Distance between point and line
Replies
1
Views
2K
Formula for Xo and Yo for graph of quadratic function
Replies
2
Views
1K
I Why does the summation come from?
Replies
11
Views
1K

Hot Threads

Recent Insights

Back
Top