Question

The dimensions of a rectangular piece of metal are (2y) by (y-7).

2. If a 1-inch by 1-inch square is removed from each corner, write an expression that
represents the area of the remaining piece of metal. Express the area in factored
form.

3. If the metal is folded to form an open box, write an expression that represents the
volume of the box. Express the volume in factored form.

Answer 1

Answer:Volume = LW - 2L - 2W + 4

Explanation:

2. If a 1-inch by 1-inch square is removed from each corner, the remaining piece of metal can be visualized as a rectangular piece with sides that are 2 inches shorter than the original piece. Let's assume the original metal piece had dimensions of length L inches and width W inches.

After removing the squares from each corner, the new length of the metal piece is (L - 2) inches, and the new width is (W - 2) inches. The area of the remaining piece of metal can be calculated by multiplying the new length and width:

Area = (L - 2) * (W - 2)

Expressing the area in factored form:

Area = LW - 2L - 2W + 4

3. If the remaining piece of metal is folded to form an open box, the volume of the box can be calculated by multiplying the area of the base with the height. Since the metal piece is folded into a box, the height of the box will be 1 inch.

The volume of the box can be expressed as:

Volume = Area * Height

= (L - 2) * (W - 2) * 1

= (L - 2)(W - 2)

Expressing the volume in factored form:

Volume = LW - 2L - 2W + 4