Answer:
k² − 4k + 4
Step-by-step explanation:
recall the following property of perfect square quadratics
(a-b)² = a²- 2ab + b² --------------( eq1)
We are given:
k² − 4k + ? --------------(eq 2)
and we are asked to determine ? for which the expression above is a perfect square.
Manipulating the given equation:
k² − 4k + ? (factor out 2 from the 2nd term), we get:
k² −(2)(k)(2) + ?
now we compare this with the right side of (eq1)
a²- 2 a b + b²
we can clearly see that a = k and b = 2,
substituting this back into eq 2,
k² − 4k + 2²
= k² − 4k + 4
