a rectangular prism has dimensions x units, 2x units, and x + 8 units. which expression represents the…

Explanation:

Step1: Recall surface - area formula

The surface - area formula of a rectangular prism with length $l$, width $w$, and height $h$ is $SA = 2(lw+lh + wh)$. Here, $l=x$, $w = 2x$, and $h=x + 8$.

Step2: Calculate $lw$

$lw=x\times2x=2x^{2}$.

Step3: Calculate $lh$

$lh=x\times(x + 8)=x^{2}+8x$.

Step4: Calculate $wh$

$wh=2x\times(x + 8)=2x^{2}+16x$.

Step5: Substitute into surface - area formula

$SA = 2(2x^{2}+x^{2}+8x+2x^{2}+16x)$.

Step6: Combine like - terms inside the parentheses

Inside the parentheses, $2x^{2}+x^{2}+2x^{2}=5x^{2}$ and $8x + 16x=24x$. So, $SA = 2(5x^{2}+24x)$.

Step7: Distribute the 2

$SA=10x^{2}+48x$.

Answer:

$10x^{2}+48x$ square units