Question

4w2 + 3W

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:

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

Step-by-step 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

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

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