Question

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?

Answer 1

8-x meters

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.