Question

1. A square floor tile has an area of (x2 + 8x +16) in2. The side length of the tile is of the form cx + d, where c and d are whole numbers.
a. Find the expression for the side length of the tile.

b. Find the expression that represents the perimeter of the tile.

c. Find the perimeter when x=8 inches.

2. Explain how you know 25n2 - 20 is not a difference of squares.

3. Explain how do you know x2 + 6x +6 is not a perfect square trinomial.

Answer 1

A)    x2 + 8x + 16
     =  x2 + 4x + 4x + 16
     = x(x+4) + 4(x+4)
     = (x+4)(x+4)               these are the equations of the two sides - they are the same because it is square. So the equation of one side is 1x + 4

b) The perimeter is the sides all added together, so that is
x+4+x+4+x+4+x+4 = x+x+x+x+4+4+4+4
                             = 4x+16 or 4(x+4)

c) When x=8 then the the perimeter is 4 lots of 8+4 inches which is 1 foot. 4 lots of 1 is 4, so the perimeter is 4 feet.

2) The difference of two squares can be written in the form x2 - y2. This can be written as (5n)2 -20, but because 20 is not a square number it can't be written as something-squared.