Question

Please help me get the answer to this problem.

Answer 1

Remember that \(a -2x\) is the width and \(b-2x\) is the height.

Answer 2

We are cutting out an x by x square from the box on all corners. Subtract 2 times this length from each side and implement the normal volume function, using x as the height.

Answer 3

So the volume would be: \[
V(x) = (a-2x)(b-2x)x
\]

Answer 4

Since \(a=40\) and \(b=60\) that means: \[
V(x)=(40-2x)(60-2x)x
\]

Answer 5

I get everything but the x outside of the equation (60-2x)x?

Answer 6

That \(x\) comes from the height of the box.

Answer 7

and when working it out I get

\[V(x)=4x(x^2-23x+600)\]

Answer 8

You can keep distributing if you want to expand all the way.

Answer 9

Mean 32x*

Answer 10

I thought it said to factor it.

Answer 11

I would completely factor it as: \[
V(x) = 4x(x-20)(x-30)
\]

Answer 12

Now, if you want to do something a little bit more fun, take the derivative of \(V(x)\) and set it equal to 0 to find the optimal magnitude for x!

Answer 13

Thank you @wio