Expand and simplify

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March 9th 2010, 09:11 PM
brumby_3

Expand and simplify

a) (x+1/y)^2
b) (x-(1/3y)+(2/5z))^2
March 9th 2010, 09:19 PM
Prove It

Quote:

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 $\frac{2}{5}z$ ?
March 9th 2010, 09:27 PM
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
???
March 9th 2010, 09:37 PM
Prove It

Quote:

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 $x\left(\frac{1}{y}\right) = \frac{x}{y}$ .
March 9th 2010, 09:39 PM
brumby_3

Cool, so my final answer for the first one is x^2 + (2x/y) + (1/y)^2
Am I right?
March 9th 2010, 09:57 PM
Prove It

Quote:

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 $\left(\frac{1}{y}\right)^2 = \frac{1}{y^2}$ .
March 10th 2010, 09:29 AM
Arcane10

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

Answer= x^2+2x/y+1/y
March 10th 2010, 04:59 PM
Prove It

Quote:

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

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

1. There was no need to post this, as the question had already been solved.

2. If you're going to post a full solution, at least make sure you get it right...

$\left(x + \frac{1}{y}\right)^2 = x^2 + \frac{2x}{y} + \frac{1}{y\color{red}^2}$ .
March 12th 2010, 08:05 AM
Arcane10

and it was right
March 12th 2010, 04:18 PM
Prove It

No it wasn't.

Reread my post, you'll notice something you missed.

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