If \( x=2, y=3 \) and \( z=5 \), evaluate the following expressions. \( \begin{array}{llll}\text { a) } x+y-z & \text { b) } x-2 y+z & \text { c) } 5(x+y-3 z) & \text { d) } 3(z-x-y) \\ \begin{array}{llll}\text { e) } x^{2}+y^{2}-z^{2} & \text { f) }(2 x-y+z)^{3} & \text { g) }(2 x-4 y+3 z)^{2} & \text { h) } \frac{x^{2}-y^{2}+}{x y z} \\ \text { i) } \frac{(x-y+z)^{2}}{x^{3}} & \text { j) } \frac{x}{y}+\frac{y}{z} & \text { k) } \frac{x}{y}-\frac{y}{z} & \text { l) }(2 x-y)^{2}+z\end{array}\end{array} \)

Given \( x = 2 \), \( y = 3 \), and \( z = 5 \), let's evaluate each expression step by step. ### a) \( x + y - z \) \[ 2 + 3 - 5 = 0 \] ### b) \( x - 2y + z \) \[ 2 - 2(3) + 5 = 2 - 6 + 5 = 1 \] ### c) \( 5(x + y - 3z) \) \[ 5(2 + 3 - 3 \times 5) = 5(5 - 15) = 5(-10) = -50 \] ### d) \( 3(z - x - y) \) \[ 3(5 - 2 - 3) = 3(0) = 0 \] ### e) \( x^2 + y^2 - z^2 \) \[ 2^2 + 3^2 - 5^2 = 4 + 9 - 25 = -12 \] ### f) \( (2x - y + z)^3 \) \[ (2 \times 2 - 3 + 5)^3 = (4 - 3 + 5)^3 = 6^3 = 216 \] ### g) \( (2x - 4y + 3z)^2 \) \[ (2 \times 2 - 4 \times 3 + 3 \times 5)^2 = (4 - 12 + 15)^2 = 7^2 = 49 \] ### h) \( \frac{x^2 - y^2}{xyz} \) \[ \frac{2^2 - 3^2}{2 \times 3 \times 5} = \frac{4 - 9}{30} = \frac{-5}{30} = -\frac{1}{6} \] ### i) \( \frac{(x - y + z)^2}{x^3} \) \[ \frac{(2 - 3 + 5)^2}{2^3} = \frac{4^2}{8} = \frac{16}{8} = 2 \] ### j) \( \frac{x}{y} + \frac{y}{z} \) \[ \frac{2}{3} + \frac{3}{5} = \frac{10}{15} + \frac{9}{15} = \frac{19}{15} \] ### k) \( \frac{x}{y} - \frac{y}{z} \) \[ \frac{2}{3} - \frac{3}{5} = \frac{10}{15} - \frac{9}{15} = \frac{1}{15} \] ### l) \( (2x - y)^2 + z \) \[ (2 \times 2 - 3)^2 + 5 = (4 - 3)^2 + 5 = 1^2 + 5 = 6 \] --- **Summary of Results:** - **a)** \( 0 \) - **b)** \( 1 \) - **c)** \( -50 \) - **d)** \( 0 \) - **e)** \( -12 \) - **f)** \( 216 \) - **g)** \( 49 \) - **h)** \( -\frac{1}{6} \) - **i)** \( 2 \) - **j)** \( \frac{19}{15} \) - **k)** \( \frac{1}{15} \) - **l)** \( 6 \)