How do you expand (x-4) ^2?

Answer: x^2 - 8x + 16

Let y = x-4

(x-4) ^2 = (x-4) * (x-4)

(x-4) ^2 = y * (x-4) ... replace one copy of (x-4) with y

(x-4) ^2 = x*y - 4*y ... distribute

(x-4) ^2 = x * (y) - 4 (y)

(x-4) ^2 = x (x - 4) - 4 (x - 4) ... replace y with x-4

(x-4) ^2 = x^2-4x-4x+16 ... distribute

(x-4) ^2 = x^2 - 8x + 16

(x - 4) ^2 = x^2 - 8*x + 16

Step-by-step explanation:

(a - b) ^2 = a^2 - 2*a*b + b^2

(x - 4) ^2 = x^2 - 2*x*4 + 4^2 = x^2 - 8*x + 16