Question 968351
the length of the box will be 20 - 2x.
the width of the box will be 10 - 2x.
the height of the box will be x.


the volume of the box is length * width * height.


this would become v = (20-2x) * (10-2x) * x


you would then simplify this by performing the indicated operations to get:


v = (200 - 40x - 20x + 4x^2) * x which would become:


v = (200 - 60x + 4x^2) * x which would become:


v = 200x - 60x^2 + 4x^3 which would then be written in standard form as:


v = 4x^3 - 60x^2 + 200x.


for example:


assume the value of x is 2.


the length of the box after cutting out the corners is equal to 20 - 4 = 16.
the width of the box after cutting out the corners is equal to 10 - 4 = 6.
the height of the box is equal to 2.


the volume is 16 * 6 * 2 = 192.


per the formjula of y = 4x^3 - 60x^2 + 200x, when you replace x with x, you get y = 4(2)^3 - 60*(2)^2 + 200*(2) which results in y = 4*8 - 60*4 + 200*2 which results in y = 32 - 240 + 400 which results in y = 192.


the formula check out ok.