Precalc Word Problem Help

Question

College Precalc, just can't figure this out

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 4 more inches off each edge.

(a) Express the final area (A) of the carpet in square inches (after both trim jobs) as a polynomial function of x.

(b) How many square inches of material were removed in the first trim job? Express the area removed in the first trim job (T1) as a function of x.

(c) How many square inches of material were removed in the second trim job? Express the area removed in the second trim job (T2) as a function of x.

Answer 1

At first the area is x² by trimming 4 inches off each of 4 edges, the new area is (x-8)². then another 4 inches off leaves the area =A = (x-16)² = x²-32x+256 square inches

The area removed in the first trim job was 4x twice + 2(x-8)(4) = 8x+8x-64=16x-64 square inches

check that by finding the area of what's left, then add what was removed, and the sum should be the original area A=x² The area left after the first trim is (x-8)²=x²-16x+64. It's now an x-8 by x-8 square.

The area left after the 2nd trimming is (x-16)²=x²-32x+256. So the area removed in two trimmings was 32x-256. Those two sum to the original x² total area removed minus area removed in 1st trim = area removed in 2nd trim. 32x-256 minus 16x-64 = 16x-192

The area removed in the 2nd trimming was 4(x-8) twice + 2(x-16)(4) = 8x-64 +8x-128 = 16x-192 square inches