Question

4w2 + 3W

- 1

5w - 2

Which expression represents the area in square feet that the homeowner will cover with fertilizer?

Answer 1

Question:

A homeowner is building a flower bed in the backyard. He plans to put a layer of fertilizer over the entire flower bed.

`Length = 4w^2 + 3w - 1`

`Width = 5w - 2.`

Which expression represents the area in square feet that the homeowner will cover with fertilizer?

Answer:

`Area = 20w^3 + 7w^2 - 11w + 2`

Explanation:

Given

`Length = 4w^2 + 3w - 1`

`Width = 5w - 2.`

Required

Determine an expression for the area

Area is calculated as:

`Area = Length *Width`

`Area = (4w^2 + 3w - 1) * (5w - 2)`

Expand

`Area = 20w^3 + 15w^2- 5w - 8w^2 - 6w + 2`

Collect like terms

`Area = 20w^3 + 15w^2- 8w^2 - 5w - 6w + 2`

`Area = 20w^3 + 7w^2 - 11w + 2`