Question

The volume of a rectangular solid (a box) can be found using the formula V = l ⋅ w ⋅ h where l is the length, w is the width, and h is the height. You measure a box to be 8 x + 2 inches wide, 6 x + 7 inches long, and 3 inches tall. What is the volume of the box?

Answer 1

Volume = 144x² + 204x + 42

Explanation:

Whenever they give you a volume problem, immediately aim to multiply every value they give you together. It doesn't matter the order. We can do the hardest part first: (8x + 2) (6x + 7). So we can multiply these two out via the Foil Method, which is basically multiplying every term in the second set of parentheses by both of the terms in the first set. Doing this will get us 48x² + 56x + 12x + 14. From here, we can combine like terms to get 48x² + 68x + 14. Now, all we have to do is multiply this value by the third value, which is just 3. So we'll multiply every term in that equation by 3 to get our final answer, 144x² + 204x + 42.

Remember, that you can multiply any type of value by any type of value, but you can only add/subtract like terms.

Hope this helps!