Question: Simplify the following expression.

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

this whole equation is divided by

5^n

Answer; 5^n+1

Remarks: I have tried doing this question twice but both attempts were unsuccesful. Please help.

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- Jun 16th 2010, 10:12 AMeconloverAn algebra question
Question: Simplify the following expression.

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

this whole equation is divided by

5^n

Answer; 5^n+1

Remarks: I have tried doing this question twice but both attempts were unsuccesful. Please help. - Jun 16th 2010, 10:28 AMearboth
- Jun 16th 2010, 10:33 AMeconloverslight 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? - Jun 16th 2010, 10:39 AMSpringFan25
considering the numerator (top of fraction) only:

$\displaystyle 4 . 5^{2n} + 5^{2n} = (4+1).5^{2n} = 5 \times 5^{2n} = 5^{2n+1}$ - Jun 16th 2010, 10:41 AMeconlover
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 - Jun 16th 2010, 10:47 AMeconlover
Still don't understand this step. Where did the 1 come from ? What about the positive sign?

Can someone explain? Thanks! - Jun 16th 2010, 11:18 AMSpringFan25
it is only factorising. i was not interpreting your dot as a decimal.

in general:

4x + x = (4+1)x = 5x

You have

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

Which says: "4 lots of $\displaystyle 5^{2n}$ plus 1 lot of $\displaystyle 5^{2n}$" equals "5 lots of $\displaystyle 5^{2n}$" - Jun 17th 2010, 01:03 PMbjhopper