# Thread: the square of a sum

1. ## the square of a sum

the problem is (c+3/c)^2 I'm trying to use the rules so i squared the first term c^2 then this is where i get stuck, double the product of the two terms, its 6 right? then square the last term which would be 9/c^2 do the c^2 cancel out to make the answer 6+9? i tried 15 as my answer on the online system and it was wrong. i only have a few more tries left and I'm not sure what else i could do to solve the problem?

2. ## Re: the square of a sum

Originally Posted by hannah2329
the problem is (c+3/c)^2 I'm trying to use the rules so i squared the first term c^2 then this is where i get stuck, double the product of the two terms, its 6 right? then square the last term which would be 9/c^2 do the c^2 cancel out to make the answer 6+9? i tried 15 as my answer on the online system and it was wrong. i only have a few more tries left and I'm not sure what else i could do to solve the problem?
No, the c^2 does not cancel.

3. ## Re: the square of a sum

Hello there,

I assume that the expression is:

$\displaystyle \left(c + \frac{3}{c}\right)^2$.

As you said correctly, square the first term:

$\displaystyle c^2$.

Next, double the product of the two terms:

$\displaystyle 2 \times c \times \frac{3}{c}$

Finally, square the last term to get:

$\displaystyle \frac{c^2}{9}$.

Notice that when you add only the first and third term above together, you get:
(I ignore the second term just so you can see the expression below)

$\displaystyle c^2 + \frac{1}{9}c^2$.

Do you see anything that can be simplified? In other words, does anything actually cancel?

I hope that this helps.

4. ## Re: the square of a sum

In general, $\displaystyle (a+ b)^2= a^2+ 2ab+ b^2$. Here, a= c and $\displaystyle b= \frac{3}{c}$ so $\displaystyle a^2= c^2$ and $\displaystyle b^2= \frac{9}{c^2}$. What is 2ab?