Answer:
Step-by-step explanation:
Area of a rectangle = Length * Width
Given the dimension
Length = 4x2 + 3x + 12
Width = 4x – 2
A) Area = (4x^2 + 3x + 12)(4x – 2)
Open the parenthesis
= 16x^3-8x^2+12x^2-6x+48x-24
Area of land in Mathville = 16x^3+4x^2+42x-24
For the land in Algebratown
Area = (5x^2 + x – 4)(2x + 1)
Area = 10x^3+5x^2+2x^2+x-8x-4
Area = 10x^3+7x^2-7x-4
B) difference between the area of Mathville and the area of Algebratown
= 16x^3+4x^2+42x-24 -(10x^3+7x^2-7x-4)
= 16x^3+4x^2+42x-24 -10x^3-7x^2+7x+4
collect like terms
= 16x^3-10x^3+4x^2-7x^2+42x+7x-24+4
= 6x^3-3x^2+49x-20
C) The difference if x = 9
Substitute x = 9 into the resulting function
A(x) = 6x^3-3x^2+49x-20
A(9) = 6(9)^3-3(9)^2+49(9)-20
A(9) = 2187-243+441-20
A(9) = 2,365
Hence the difference of the areas if x = 9 is 2,365
