A carpenter needs to build a box to hold his wood screws. He has a sheet of wood that measures 18 inches by 12 inches. He then cuts equal squares from each corner. (a) Write an expression for the length, width, and height for the open box. (b) Write a function for the volume (use factored form).

The expressions for the length, width, and height are 18 - 2x, 12 - 2x, and x while the volume function is V = (12 - 2x)(18 - 2x)x(a) How to determine the expression for the length, width, and heightFrom the question, we have the following parameters:Dimension of sheet = 8 inches by 12 inchesAlso from the question, we understand that:He cuts equal squares from each corner. The cut-out length from the sheet would represent the height of the boxRepresent this cut-out length with xSo, we haveHeight = xThe width and the length are then represented asWidth = Initial width - 2xLength = Initial length - 2xSo, we haveWidth = 12 - 2xLength = 18 - 2x(b) Write a function for the volumeThe volume of a box is the product of its dimensionsIn this case, we haveWidth = 12 - 2xLength = 18 - 2xHeight = xSo, we haveVolume = Width * Length * Height Substitute the known values in the above equation So, we have the following equationV = (12 - 2x)(18 - 2x)xSo, the volume function is V = (12 - 2x)(18 - 2x)xRead more about volumes athttps://brainly.com/question/463363#SPJ1