A large square carpet is initially x inches long and x inche

A large square carpet is initially x inches long and x inches wide. Randy decides to trim 4 inches off each edge of the carpet because the edges are worn. Later he goes back and trims 3 more inches off each edge. Express the final area (A) of the carpet in square inches (after both trim jobs) as a polynomial function of x. A(X) = How many square inches of material were removed in the first trim job Express the area removed in the first trim job (T_1) as a function of x, T_1(x) = How many square inches of material were removed in the second trim job Express the area removed in the second trim job (T_2) as a function of x, T_2(x) =

Solution

Sqaure carpet with eges ---x inches

trim by 4 inces ---- x-4

Further trim by 3 inches ----- x -4 -3 = x-7

So, Area(x) = edge^2 = (x-7)^2

b) In first part 4 inches were removed So, trimmed area = (x-4)^2

Material remonved -= x^2 -(x-4)^2 = x^2 - x^2 - 16 +8x = 8x -16

c) In second part 3 inches were removed:So, triimed area = ( x-7)^2

Material removed : (x-4)^2 - (x -7)^2 = x^2 +16 -8x -x^2 -49 +14x

= -33 +6x