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Simplifying

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joshdelayslahsc:
Hi all,

I'm so confused on when and where to distribute stuff on algebra.

Example:

2(4x) = 8x; however, if I'm trying to simplify stuff and it looks like this: 3(x^2y^2)^3; it would be 3(x^6y^6) then you don't need to distribute it. The final would be 3x^6y^6.

My question is when should you distribute and when to just remove the brackets.

Cheers

fun_jirachi:
Welcome to the forums!!!!
I reckon in the examples provided you've just distributed as you say because you haven't got a coefficient in the term in the brackets? I think its best to distribute all the time, as even when you just need to remove the brackets, you'd still get the same answer. Removing the brackets isn't that much faster, it's just a matter of seeing if there's a coefficient there or not.

That's my take, hope I helped! :D

RuiAce:

--- Quote from: joshdelayslahsc on September 26, 2018, 04:28:23 pm ---Hi all,

I'm so confused on when and where to distribute stuff on algebra.

Example:

2(4x) = 8x; however, if I'm trying to simplify stuff and it looks like this: 3(x^2y^2)^3; it would be 3(x^6y^6) then you don't need to distribute it. The final would be 3x^6y^6.

My question is when should you distribute and when to just remove the brackets.

Cheers

--- End quote ---
The problem with the word distribute in this context is that it's basically too vague. Distribute can mean many things.

Your first example, \(2 (4x) = 8x\), is an example of the distributive law \(a(b+c) = ab + ac\). You let \(a = 2\), \(b = 4x\) and \(c = 0\), so that \( 2(4x + 0) = 8x + 0\). Of course, then +0's then disappear.

The next one features an index law. The index law relevant to this question is \( (ab)^m = a^m b^m\). It looks like "distributing", but it's not the same type of distribution, rather this is a theorem.
Of course, in your case, you have \( (x^2y^2)^3 \) = \( (x^2)^3 (y^2)^3 \).

(In particular, this becomes \(x^6y^6\) like you have stated. This is because you've now used yet another index law: \( (a^m)^n = a^{mn} \).)

That aside, just see the above post for a response to your main question

joshdelayslahsc:

--- Quote from: RuiAce on September 26, 2018, 07:20:36 pm ---The problem with the word distribute in this context is that it's basically too vague. Distribute can mean many things.

Your first example, \(2 (4x) = 8x\), is an example of the distributive law \(a(b+c) = ab + ac\). You let \(a = 2\), \(b = 4x\) and \(c = 0\), so that \( 2(4x + 0) = 8x + 0\). Of course, then +0's then disappear.

The next one features an index law. The index law relevant to this question is \( (ab)^m = a^m b^m\). It looks like "distributing", but it's not the same type of distribution, rather this is a theorem.
Of course, in your case, you have \( (x^2y^2)^3 \) = \( (x^2)^3 (y^2)^3 \).

(In particular, this becomes \(x^6y^6\) like you have stated. This is because you've now used yet another index law: \( (a^m)^n = a^{mn} \).)

That aside, just see the above post for a response to your main question

--- End quote ---

--- Quote from: fun_jirachi on September 26, 2018, 04:55:22 pm ---
Welcome to the forums!!!!
I reckon in the examples provided you've just distributed as you say because you haven't got a coefficient in the term in the brackets? I think its best to distribute all the time, as even when you just need to remove the brackets, you'd still get the same answer. Removing the brackets isn't that much faster, it's just a matter of seeing if there's a coefficient there or not.

That's my take, hope I helped! :D

--- End quote ---

Thank you so much. It makes sense now.

Also, I've got this question and I can't really figure out.

The question is: simplify, write the answers with positive indices.

3^2n*25^2n-1 / 15^n-1

I don't know how to do this.

RuiAce:

--- Quote from: joshdelayslahsc on September 26, 2018, 07:57:59 pm ---Thank you so much. It makes sense now.

Also, I've got this question and I can't really figure out.

The question is: simplify, write the answers with positive indices.

3^2n*25^2n-1 / 15^n-1

I don't know how to do this.


--- End quote ---
It's very hard to interpret what's going on. When I read this I see \( 3^2 n \times 25^2 n-\frac{1}{15^n} - 1 \).

Please use brackets to indicate what goes with what

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