Question

A rectangle has the height of n^3 + 4n^2 and the width of n^3 + 5n^2

Answer 1

To find the area of a rectangle, multiply the height by the width. The given dimensions are in polynomial form, and the resulting area is a polynomial expression.

Step-by-step explanation:

The student's question relates to finding the area of a rectangle. The area is calculated by multiplying the rectangle's height and width. Given that the height of the rectangle is n^3 + 4n^2 and the width is n^3 + 5n^2, the area of the rectangle would be:

(n^3 + 4n^2) * (n^3 + 5n^2) = n^6 + 5n^5 + 4n^5 + 20n^4 = n^6 + 9n^5 + 20n^4.

This is a polynomial expression that represents the area of the rectangle when n terms are factors of the dimensions. This problem involves algebraic manipulation to expand the product of two polynomials.