1. ## An algebra question

Question: Simplify the following expression.

(2x5^n)^2 + 25^n

this whole equation is divided by

5^n

2. Originally Posted by econlover
Question: Simplify the following expression.

(2x5^n)^2 + 25^n

this whole equation is divided by

5^n

1. Use the laws of powers:

$\frac{(2 \cdot 5^n)^2 + 25^n}{5^n} = \frac{4 \cdot 5^{2n} + 5^{2n}}{5^n}= \frac{5 \cdot 5^{2n}}{5^n}=5 \cdot 5^n = 5^{n+1}$

3. ## slight question

Thanks.

I understand most of it but how did you move along from the 1st step of your answer to the second one

that is, in specific terms, where did the 4 go?

4. considering the numerator (top of fraction) only:
$4 . 5^{2n} + 5^{2n} = (4+1).5^{2n} = 5 \times 5^{2n} = 5^{2n+1}$

5. Thanks for the message. But I guess you misinterpret the sign of this "."

It is not 4.5 (4 decimal 5) but 4 . 5 meaning 4 x 5 = 4 times 5

Hope this clears up the misconception

6. Still don't understand this step. Where did the 1 come from ? What about the positive sign?

Can someone explain? Thanks!

7. it is only factorising. i was not interpreting your dot as a decimal.

in general:
4x + x = (4+1)x = 5x

You have
$4 \times 5^{2n} + 1 \times 5^{2n}$ = $5 \times 5^{2n}$

Which says: "4 lots of $5^{2n}$ plus 1 lot of $5^{2n}$" equals "5 lots of $5^{2n}$"

8. Originally Posted by econlover
Question: Simplify the following expression.

(2x5^n)^2 + 25^n

this whole equation is divided by

5^n