Question

A rectangular tract of land in Mathville has the dimensions 4x2 + 3x + 12 and 4x – 2. Another rectangular area of a land in Algebratown has dimensions 5x2 + x – 4 and 2x + 1.

A)Find the area of each using the box method in terms of x
B)What is the difference between the area of Mathville and the area of Algebratown?
C)hat is the difference of the areas if x = 9?

Answer 1

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