1. **State the problem:** Find expressions for the total surface area and volume of a rectangular packing crate with dimensions: Length = $2x$ Width = $x$ Height = $2x + 2$ 2. **Surface area formula for a rectangular prism:** $$\text{Surface Area} = 2(lw + lh + wh)$$ where $l$ is length, $w$ is width, and $h$ is height. 3. **Calculate each product:** $$lw = (2x)(x) = 2x^2$$ $$lh = (2x)(2x + 2) = 4x^2 + 4x$$ $$wh = (x)(2x + 2) = 2x^2 + 2x$$ 4. **Sum the products:** $$lw + lh + wh = 2x^2 + (4x^2 + 4x) + (2x^2 + 2x) = (2x^2 + 4x^2 + 2x^2) + (4x + 2x) = 8x^2 + 6x$$ 5. **Multiply by 2 for total surface area:** $$\text{Surface Area} = 2(8x^2 + 6x) = 16x^2 + 12x$$ 6. **Volume formula for a rectangular prism:** $$\text{Volume} = l \times w \times h$$ 7. **Calculate volume:** $$\text{Volume} = (2x)(x)(2x + 2) = 2x^2(2x + 2) = 2x^2 \times 2(x + 1) = 4x^2(x + 1) = 4x^3 + 4x^2$$ **Final answers:** - Surface area: $$16x^2 + 12x$$ - Volume: $$4x^3 + 4x^2$$