The square below has an area of

64

-

16

x

+

x

2

64-16x+x

2

64, minus, 16, x, plus, x, squared square meters.

What expression represents the length of one side of the square?

8-x meters

Step-by-step explanation:

Both 64 and x^2 are perfect squares, since 64 = (8) ^2 and x^2 = (x) ^2.

Additionally, 16x is twice the product of the roots of 64 and x^2, since 16x=2 (8) (x).

So we can use h the square of a difference pattern to factor:

a^2-2 (a) (b) + b^2 = (a-b) ^2

In this case, a=8 and b=x:

(8) ^2-2 (8) (x) + (x) ^2 = (8-x) ^2

In conclusion ...

64-16x+x^2 = (8-x) ^2

So the side length of the square is 8-x meters.