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

Answer:

A: $-w^{2}+6w+17$

B: $5w^{2}+14w+7$

Step-by-step 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 $5w^{2}+14w+7$.