Answer:
The area = w^4 + 3w^3 + 11w^2 + 6w + 18.
Step-by-step 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.
Answer:
Step-by-step 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
