Answer
$16$.
Work Step by Step
The given expression is
$kx^2+8xy+y^2$
Use the algebraic expression.
$a^2+2ab+b^2=(a+b)^2$.
Factor the middle term of the given expression as shown below.
$8xy = 2(4x)(y)$
Compare the above term with the algebraic expression.
$2ab=2(4x)(y)$
We have $a=4x$ and $b=y$.
Therefore $kx^2=a^2$.
Plug all values.
$kx^2=(4x)^2$.
Simplify.
$kx^2=16x^2$.
Divide both side by $x^2$.
$k=16$.
