if the trinomial n^2-12kn+r, what is the value of r

Question

Perfect squares

Answer 1

If (n+a) is squared, we get n^2 + 2na + a^2.

So, if n^2-12kn+r is a perfect square, then we can equate n^2 + 2na + a^2 witrh n^2 - 12kn + r, and by comparing coefficients we get

2a = -12k  ------ (1)

a^2 = r    -------- (2)

from (1), a = -6

putting a = -6 into (2) gives us r = 36. If the given trinomial is a perfect square, then that square is

(n - 6)^2