1. simplify

1. Simplify the following expressions:

a) (5x - y)^2 - (x - 5y)^2 / -4x - 4y

b) (4x^3y^5z^4)^4 / (2x^3y^2z^4)^2

c) x^3y9(^6/5) 5squarerootx^-10y^11

2. Originally Posted by princess_anna57
1. Simplify the following expressions:

a) (5x - y)^2 - (x - 5y)^2 / -4x - 4y

b) (4x^3y^5z^4)^4 / (2x^3y^2z^4)^2

c) x^3y9(^6/5) 5squarerootx^-10y^11
please use parenthesis to clarify what you mean.

should (a) be (5x - y)^2 - (x - 5y)^2 /(-4x - 4y) ?

as in $\displaystyle (5x - y)^2 - \frac {(x - 5y)^2 }{-4x - 4y}$

and for (c), is it $\displaystyle 5 \sqrt {x^{-10}y^{11}}$ ?

3. Yup

Yup they are all rightly written. Sorry about not adding the parenthesis. I'm new to the whole typing equations thing -blush-

4. Originally Posted by princess_anna57
b) (4x^3y^5z^4)^4 / (2x^3y^2z^4)^2
$\displaystyle \frac {(4x^3 y^5 z^4)^4}{(2x^3 y^2 z^4)^2}$

$\displaystyle = \frac {4^4 x^{12} y^{20} z^{16}}{2^2 x^6 y^4 z^8}$

since when we raise a base to a power, we multiply the powers.

$\displaystyle 64 x^{12 - 6} y^{20 - 4} z^{16 - 8}$

since when we divide numbers of the same base, we subtract the powers.

$\displaystyle = 64x^6 y^{16} z^8$

5. Originally Posted by princess_anna57
Yup they are all rightly written. Sorry about not adding the parenthesis. I'm new to the whole typing equations thing -blush-
you're sure it's not $\displaystyle \sqrt [5] {x^{-10}y^{11}}$, because it seems awkward to me to have a 5 there

6. Oops.

Yeah it's the little five and before that is x3y(^6/5)

So y's to the power of 6/5

7. Originally Posted by princess_anna57
c) x^3y9(^6/5) 5squarerootx^-10y^11
$\displaystyle x^3 y^{ \frac {6}{5}} \sqrt [5] {x^{-10} y^{11}}$

$\displaystyle = x^3 y^{\frac {6}{5}} \left( x^{-10} y^{11} \right)^{ \frac {1}{5}}$

$\displaystyle = x^3 y^{ \frac {6}{5}} x^{-2} y^{ \frac {11}{5}}$

$\displaystyle = x y^{ \frac {17}{5}}$

If you don't understand anything, please say so.

I can't really see a way to simplify the first one. it just seems to get more messy to me

8. Ohh I just realised with the first one:

The first part of the equation is supposed to be up the top too with the (x-5y)^2. Omg how did I not pick that up. Tired already? Sheesh.

9. Originally Posted by princess_anna57
Ohh I just realised with the first one:

The first part of the equation is supposed to be up the top too with the (x-5y)^2. Omg how did I not pick that up. Tired already? Sheesh.
It's not that late where you are now. how can you be tired? that's what not using parenthesis gets you. ok, let's try again.

$\displaystyle \frac {(5x - y)^2 - (x - 5y)^2}{-4x - 4y}$

$\displaystyle = \frac {25x^2 - 10xy + y^2 - x^2 + 10xy - 25y^2}{-4(x + y)}$

$\displaystyle = \frac {24x^2 - 24y^2}{-4(x + y)}$

$\displaystyle = \frac {24(x^2 - y^2)}{-4(x + y)}$

$\displaystyle = \frac {-6(x + y)(x - y)}{(x + y)}$

$\displaystyle = -6(x - y)$

$\displaystyle = 6(y - x)$

You probably should double check your questions to make sure i answered the right ones and not typos

10. Sorry but it's hard typing these equations out. they're all written correctly. Thanks!

11. Originally Posted by princess_anna57
1. Simplify the following expressions:

a) (5x - y)^2 - (x - 5y)^2 / -4x - 4y

...
Hello,

I assume that you mean:

$\displaystyle \frac{(5x-y)^2-(x-5y)^2}{-4x-4y}=\frac{25x^2-10xy+y^2-x^2+10xy-25y^2}{-4(x+y)}$ = $\displaystyle \frac{24(x^2-y^2)}{-4(x+y)} = \frac{24(x+y)(x-y)}{-4(x+y)}= -6(x-y) = 6y-6x$

EDIT: You are typing to fast for me, Jhevon

12. Originally Posted by earboth
EDIT: You are typing to fast for me, Jhevon
Nah, I just started typing long before you did