Augustina has 2 posters with length x inches. One poster has a width of xplus+22 ​inches, and the other has a width of xplus+55 inches. Write an expression to represent the area of wall that the posters will cover.



Answer :

Answer:

2x² + 77x  (square inches)

Step-by-step explanation:

The area of the wall covered by both posters is the sum of the areas covered by each poster

Each poster has a rectangular shape

The area of a rectangle of length L and width W inches is their product: LW

The length of each poster is L = x inches

Area of the first poster

The first poster has length L = x inches and width W = x + 22 inches

Therefore the area of the first poster = LW
= x (x + 22)  

= x² + 22x   (square inches)

Area of second poster

The length of the second poster is L = x inches and width W = x + 55 inches

Area of second poster = LW

= x ( x + 55)

= x² + 55x             (square inches)

Total of both areas

Total area covered by both posters
= (x² + 22x) + (x² + 55x)

= x² + 22x + x² + 55x

= x² + x² + 22x + 55x      grouping like terms

= 2x² + 77x                     add like terms

Answer: 2x² + 77x (square inches)