Question

Jocelyn and Lorlesha are comparing the size of their villages in the Clash of Clans app. The area of Jocelyn's village is represented by the polynomial, 2w2+10w+12. the area of lorleshas village is represented by the polynomial, 3w2+4w-5, where e represents the width, in meters of their Town hall.

part A: find the expression that represents the additional area Jocelyns village.

part B: find the expression that represents the combined total area of their villages.

Answer 1

A:
`-w^(2)+6w+17`

B:
`5w^(2)+14w+7`

Explanation:

We have been given that the area of Jocelyn's village is represented by the polynomial
`2w^(2)+10w+12`. The area of Lorlesha's village is represented by the polynomial
`3w^(2)+4w-5`, where w represents the width, in meters of their Town hall.

A: To find the expression that will represent the additional area of Jocelyn's village, we will subtract the total area of Lorlesha's village from the total area of Jocelyn's village.

`\text{Additional area of Jocelyn's village}=2w^(2)+10w+12-(3w^(2)+4w-5)`

Let us distribute negative sign to simplify our expression.

`\text{Additional area of Jocelyn's village}=2w^(2)+10w+12-3w^(2)-4w+5`

Upon combining like terms we will get,

`\text{Additional area of Jocelyn's village}=2w^(2)-3w^(2)+10w--4w+12+5`

`\text{Additional area of Jocelyn's village}=(2-3)w^(2)+(10-4)w+12+5`

`\text{Additional area of Jocelyn's village}=-w^(2)+6w+17`

Therefore, the expression that represents the additional area Jocelyn's village is
`-w^(2)+6w+17`.

B: To find the expression that represents the combined total area of their villages we will add areas of Jocelyn's and Larlesha's village.

`\text{Combined total area}=2w^(2)+10w+12+(3w^(2)+4w-5)`

Upon combining like terms we will get,

`\text{Combined total area}=2w^(2)+3w^(2)+10w+4w+12-5`

`\text{Combined total area}=(2+3)w^(2)+(10+4)w+12-5`

`\text{Combined total area}=5w^(2)+14w+7`

Therefore the expression represents the combined total area of their villages is
`5w^(2)+14w+7`.