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6 December, 15:11

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

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Answers (2)
  1. 6 December, 15:22
    0
    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.
  2. 6 December, 15:28
    0
    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
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