How was (3^3 * 5^4 + 3^2 * 5^4) / (3 * 5^4) rearranged ?

[Alqus]

Hello, I have a problem : (3^3 * 5^4 + 3^2 * 5^4) / (3 * 5^4) . My teacher rearranged it to : (3^2 * 5^4 * (3 + 1)) / (3 * 5^4). Could someone please explain to me how this was done ?

 

[Deleted member 4993]

Hello, I have a problem : (3^3 * 5^4 + 3^2 * 5^4) / (3 * 5^4) . My teacher rearranged it to : (3^2 * 5^4 * (3 + 1)) / (3 * 5^4). Could someone please explain to me how this was done ?

Hint: 3^3 = 3^2 * 3

Then factorize the numerator.

 

[stapel]

Hello, I have a problem : (3^3 * 5^4 + 3^2 * 5^4) / (3 * 5^4) . My teacher rearranged it to : (3^2 * 5^4 * (3 + 1)) / (3 * 5^4). Could someone please explain to me how this was done ?

You were given this:

. . . . .\(\displaystyle \dfrac{3^3\, \cdot\, 5^4\, +\, 3^2\, \cdot\, 5^4}{3\, \cdot\, 5^4}\)

What did you get as the greatest common factor of the numerator, when you did the factorization? What did you get for the remaining terms when you took the GCF out front?

 

[Alqus]

You were given this:

. . . . .\(\displaystyle \dfrac{3^3\, \cdot\, 5^4\, +\, 3^2\, \cdot\, 5^4}{3\, \cdot\, 5^4}\)

What did you get as the greatest common factor of the numerator, when you did the factorization? What did you get for the remaining terms when you took the GCF out front?

I guess GCF is 5^4 and 3^2 ? Remaining terms 1 and 3. Just for a plain example I tried to do : 6 * 2 + 3 * 4. GCF is 2 and 3, and what remains is 2 and 2 ?

3 * 2(2+2) | is this a correct form ?

 

[stapel]

I guess GCF is 5^4 and 3^2 ? Remaining terms 1 and 3.

Yes:

. . . . .\(\displaystyle \dfrac{3^3\, \cdot\, 5^4\, +\, 3^2\, \cdot\, 5^4}{3\, \cdot\, 5^4}\, =\, \dfrac{(3^2\, \cdot\, 5^4)\, \cdot (3^1)\, +\, (3^2\, \cdot\, 5^4)\, \cdot\, (1)}{3\, \cdot\, 5^4}\, =\, \dfrac{(3^2\, \cdot\, 5^4)\, \cdot\, (3\, +\, 1)}{3\, \cdot\, 5^4}\)

Just for a plain example I tried to do : 6 * 2 + 3 * 4. GCF is 2 and 3, and what remains is 2 and 2 ?

Bad example, as 6*2 = 3*4 = 12. But, to be complete:

. . . . .\(\displaystyle 6\, \cdot\, 2\, +\, 3\, \cdot\, 4\, =\, 2\, \cdot\, 3\, \cdot\, 2\, +\, 3\, \cdot\, 2\, \cdot\, 2\, =\, 2^2\, \cdot\, 3\, +\, 3\, \cdot\, 2^2\)

The GCF is 3 * 2² = 12, with the remaining terms being 1 and 1, for two copies of 12 (which makes sense).

 

[Steven G]

I guess GCF is 5^4 and 3^2 ? Remaining terms 1 and 3. Just for a plain example I tried to do : 6 * 2 + 3 * 4. GCF is 2 and 3, and what remains is 2 and 2 ?

3 * 2(2+2) | is this a correct form ?

Please don't say that the GCF is 5^4 and 3^2, Rather say that the GCF is 5^4 * 3^2