Answer
$=x^2-40x+400$
$=(x-20)^2$
Work Step by Step
The given expression is
$=x^2-40x$
Find the value of $(\frac{b}{2})^2$.
Substitute $-40$ for $b$.
$=(\frac{-40}{2})^2$
Simplify.
$=(-20)^2$
$=400$
Add $400$ to the given expression.
$=x^2-40x+400$
Write the the polynomial as $a^2-2ab+b^2$.
$=x^2-2(x)(20)+(20)^2$
Use perfect square trinomial pattern
$a^2-2ab+b^2=(a-b)^2$
We have $a=x$ and $b=20$.
$=(x-20)^2$
$=x^2-40x+400$
$=(x-20)^2$
