Box 1: Dimensions: x by 3x by x3 Area of base = x(3x) = 3x2 Box 2: Dimensions: x by 4x – 1 by x3 Area of base = x(4x – 1) = 4x2 – x Complete the statements about the number of terms in the polynomial representing the volume of each box. Box 1's volume will be a Box 2's volume will be a . Explain your reasoning.

The volume of a box is the amount of space it can occupy.

The given parameters are:

Dimensions of box 1: x by 3x by x^3

Dimensions of box 2: x by 4x - 1 by x^3

The volume of the box is calculated by multiplying the dimensions.

So, we have:

Box 1

Box 2

Open brackets

After calculating the volumes, we have:

---- box 1

---- box 2

Hence,

Read more about volumes at:

link

Box 1's  volume will be a monomial

Box 2's volume will be a binomial

Explain your reasoning:

Box 1’s volume is modeled by a monomial times a monomial, so it will be a monomial.  Box 2’s volume is modeled by a monomial times a binomial, so it will be a binomial.

Step-by-step explanation:

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