b Use the FOIL method when finding the expressions for the areas.
C
c Use the expressions you find in Part B.
A
a x> 4
B
b The square sandbox
C
c 4 square units
Practice makes perfect
a We can build a square sandbox with a side length of x-2 and a rectangular sandbox with a width of x-4 and a length of x. The side lengths of the boxes should be greater than zero.
x-2 > 0 x > 0 x-4 > 0 ⇒ x > 2 x > 0 x > 4
If the value of x is greater than 4, all of the lengths are greater than zero. Hence, the possible values of x are x > 4.
b Let's first find the area of the square sandbox.
We see that the area of the square sandbox is 4 more than the area of the rectangular sandbox.
x^2-4x+4 > x^2-4x
Hence, the square sandbox has the greater area.
c Let's subtract the area of the rectangular sandbox from the area of the square sandbox.
& x^2-4x+4
-&(x^2-4x)
& 4
The difference is 4 square units.
