Ask yourself: what number squared gives $36$? Use that number as a candidate for $b$ in the pattern.

After picking a possible value for $b$, compute $-2ab$ with $a = x$ and see if it matches the $-12x$ term.

If you think you have the right binomial, expand it using FOIL and see if you get $x^2 - 12x + 36$.

In Desmos, type y1 = x^2 - 12x + 36 to graph the given expression.

Type each option as a separate function, for example: y2 = (x - 6)^2, y3 = (x + 6)^2, y4 = x^2 - 36, y5 = (x - 3)^2. Use the checkboxes to turn them on and off.

Look at the graphs: the correct choice will have a graph that lies exactly on top of the graph of $y1$ for all x-values (same shape, same vertex, same position). The other choices will have parabolas in different positions or with different shapes.

Pick a few x-values (for example, $x = 0$, $x = 2$, $x = 10$) and use a table in Desmos for $y1$ and for each answer choice. The equivalent expression will give the same y-values as $y1$ at every x you test.

Compare $x^2 - 12x + 36$ to the standard pattern

Here, $x^2$ matches $a^2$, so $a = x$. The constant term $36$ should match $b^2$ for some number $b$.

Since $b^2 = 36$, $b$ must be $6$ or $-6$ (because $6^2 = 36$ and $(-6)^2 = 36$). Now use the middle term, $-12x$, to decide which sign works.

Plug $a = x$ and $b = 6$ into $-2ab$:

which matches the middle term exactly.

Since $x^2 - 12x + 36$ fits the pattern $a^2 - 2ab + b^2$ with $a = x$ and $b = 6$, it factors as

So the expression equivalent to $x^2 - 12x + 36$ is $(x - 6)^2$.