From a rectangular sheet measuring $175$ mm by $150$ mm $,$ equal squares of side $x$ are cut from each of the four corners. The remaining flaps are then folded upwards to form an open box.

a$)$

Write an expression for the volume $(V)$ of the box in terms of $x.$ Fully expand all brackets

$V=,m{m}^3$

b$)$

Find the value of $x$ that gives the maximum volume and give your answer to $2$ decimal places.

$x_{\text{m}\text{a}\text{x}}=,mm$

Calculate the volume to the nearest $m{m}^3.$

$V_{\text{m}\text{a}\text{x}}=,m{m}^3$