If m^2 + n^2 = 18 and mn=7, what is (m-n) ^2

(m - n) ^2 = 4

Step-by-step explanation:

(m - n) ^2 = m^2 - 2mn + n^2 when (m-n) ^2 is expanded using foil.

But m^2 + n^2 = 18 Given

mn = 7 Given

(m - n) ^2 = m^2 + n^2 - 2 mn Substitute in the given values

(m - n) ^2 = 18 - 2*7 Reduce

(m - n) ^2 = 18 - 14 Combine

(m - n) ^2 = 4

(m-n) ^2 = m^2 - 2mn + n^2

(m-n) ^2 = m^2 + n^2 - 2mn

Substitute m^2 + n^2 = 18 and mn=7

(m-n) ^2 = 18 - 2 (7)

(m-n) ^2 = 18 - 14

(m-n) ^2 = 4