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
$\displaystyle \frac {(4x^3 y^5 z^4)^4}{(2x^3 y^2 z^4)^2}$
$\displaystyle = \frac {4^4 x^{12} y^{20} z^{16}}{2^2 x^6 y^4 z^8}$
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.
$\displaystyle = 64x^6 y^{16} z^8$
$\displaystyle x^3 y^{ \frac {6}{5}} \sqrt [5] {x^{-10} y^{11}}$
$\displaystyle = x^3 y^{\frac {6}{5}} \left( x^{-10} y^{11} \right)^{ \frac {1}{5}}$
$\displaystyle = x^3 y^{ \frac {6}{5}} x^{-2} y^{ \frac {11}{5}}$
$\displaystyle = x y^{ \frac {17}{5}}$
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
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
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