Question

factor the expression using the box method by filling in the outside of the box below. then write the factored expression.
$x^2 - 8x + 16$
show your work here
box with $x^2$, $-4x$, $-4x$, 16 and empty boxes around it

Explanation:

Step1: Find top box values

Top-left: $\gcd(x^2, -4x) = x$
Top-right: $\gcd(-4x, 16) = -4$

Step2: Find left box values

Left-top: $\gcd(x^2, -4x) = x$
Left-bottom: $\gcd(-4x, 16) = -4$

Step3: Write factored form

Combine box pairs: $(x-4)(x-4)=(x-4)^2$

Answer:

Box outside values (top-left, top-right, left-top, left-bottom): $x$, $-4$, $x$, $-4$
Factored expression: $(x-4)^2$