A square prism has square sides with area x^2+8x+16 and rectangular sides with area 2x^2+15x+28. What expression represents the surface area of the square prism

10x^2+76x+144

Step-by-step explanation:

Hi there! I'm glad I was able to help you solve this scary-looking problem! :P

Remember, the surface area of a square prism is the SUM (+) of the areas of the two square sides AND the four rectangle sides:

    (x^2+8x+16) + (x^2+8x+16) + (2x^2+15x+28) + (2x^2+15x+28) + (2x^x+15x+28) + (2x^2+15x+28)

You may be wondering why we don't just write it as (x^2+8x+16) times itself + (2x^2+15x+28) times 4, but we have to group like terms next, and in order to do that we have to see what what we're left with, as shown below:

    (x^2+x^2+2x^2+2x^2+2x^2+2x^2) + (8x+8x+15x+15x+15x+15x) + (16+16+28+28+28+28)

It may look complicated, I know, but all you have to do now for the final step is combine the like terms, resulting in your answer, 10x^2+76x+144!

I hope this helped you! If you think I've made a mistake, leave a comment below and I'll be happy to help you further! <3

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