# Math Help - Expand and simplify

1. ## Expand and simplify

a) (x+1/y)^2
b) (x-(1/3y)+(2/5z))^2

2. Originally Posted by brumby_3
a) (x+1/y)^2
b) (x-(1/3y)+(2/5z))^2
$\left(x + \frac{1}{y}\right)^2 = \left(x + \frac{1}{y}\right)\left(x + \frac{1}{y}\right)$.

FOIL it out.

I can't read the second. Has it got $\frac{1}{3y}$ and $\frac{2}{5z}$, or $\frac{1}{3}y$ and $\frac{2}{5}z$?

3. Hi Prove it,
It's the second combination.
So for the first one would it be x^2 + (1/y)x + (1/y)x + (1/y)^2 or is it x^2 + (1/xy) + (1/xy) + (1/y)^2
???

4. Originally Posted by brumby_3
Hi Prove it,
It's the second combination.
So for the first one would it be x^2 + (1/y)x + (1/y)x + (1/y)^2 or is it x^2 + (1/xy) + (1/xy) + (1/y)^2
???
The first combination.

And remember that $x\left(\frac{1}{y}\right) = \frac{x}{y}$.

5. Cool, so my final answer for the first one is x^2 + (2x/y) + (1/y)^2
Am I right?

6. Originally Posted by brumby_3
Cool, so my final answer for the first one is x^2 + (2x/y) + (1/y)^2
Am I right?
Yes. But remember that $\left(\frac{1}{y}\right)^2 = \frac{1}{y^2}$.

7. ## Solution

a) (x+1/y)^2

(x+1/y)^2 = (x+1/y)(x+1/y)

(x+1/y)(x+1/y)= x^2+x/y+x/y+1/y

x^2+x/y+x/y+1/y= x^2+2x/y+1/y

8. Originally Posted by Arcane10
a) (x+1/y)^2

(x+1/y)^2 = (x+1/y)(x+1/y)

(x+1/y)(x+1/y)= x^2+x/y+x/y+1/y

x^2+x/y+x/y+1/y= x^2+2x/y+1/y

$\left(x + \frac{1}{y}\right)^2 = x^2 + \frac{2x}{y} + \frac{1}{y\color{red}^2}$.