Question

A rectangle has a height of w2 + 3w + 9 and a width of w2 + 2.

Express the area of the entire rectangle.

Your answer should be a polynomial in standard form.
22

Answer 1

Explanation:

The formula for determining the area of a rectangle is expressed as

Area = length × width

From the information given,

Height = w² + 3w + 9

Width = w² + 2

The expression for the area would be

Area = (w² + 3w + 9)(w² + 2)

We would expand the brackets by multiplying each term in the first bracket by each term in the second bracket. It becomes

Area = w⁴ + 2w² + 3w³ + 6w + 9w² + 18

Collecting like terms, it becomes

Area = w⁴ + 3w³ + 2w² + 9w² + 6w + 18

Area = w⁴ + 3w³ + 11w² + 6w + 18

Answer 2

The area = w^4 + 3w^3 + 11w^2 + 6w + 18.

Explanation:

Area = height * width

= (w^2 + 2)(w^2 + 3w + 9)

We multiply the second bracket by w^2, then by +2:

= w^2(w^2 + 3w + 9) + 2(w^2 + 3w + 9)

= w^4 + 3w^3 + 9w^2 + 2w^2 + 6w + 18

= w^4 + 3w^3 + 11w^2 + 6w + 18.