Answer:
4x³ - 30x² + 54x
Step-by-step explanation:
Length of the rectangular cardboard = 9 inches
Width of the rectangular cardboard = 6 inches
if the square of sides x inches is cut from each corner of the rectangular cardboard and folded to make a tray, then we have
Length of the tray = length of cardboard - 2(side of square )
= 9 - 2x
Width of the tray = width of cardboard - 2( side of square)
= 6 - 2x
height of tray = sides of square
= x
volume of tray = Length × width × height
= (9 - 2x) (6 - 2x) (x)
Open the parenthesis
= (54 - 18x - 12x + 4x²)(x)
= 54x - 18x² - 12x² + 4x³
= 54x - 30x² +4x³
Re-arrange
4x³ - 30x² + 54x
Volume, V of the tray in terms of x = 4x³ - 30x² + 54x
