From the problem, the length and the width will be reduced by twice the side of the square.
The length of the box will be :
[tex]26-2x[/tex]
The width of the box will be :
[tex]20-2x[/tex]
and the height will be the measurement of the square side :
[tex]x[/tex]
Note that the volume of a box is length x width x height.
1. The volume will be :
[tex]V(x)=x(26-2x)(20-2x)[/tex]
Expand and simplify the function :
[tex]\begin{gathered} V(x)=x(26-2x)(20-2x) \\ V(x)=x(520-40x-52x+4x^2) \\ V(x)=x(4x^2-92x+520) \\ V(x)=4x^3-92x^2+520x \end{gathered}[/tex]
2. Graph the function using desmos.
