Simplify (x^2 - y^2)^2 when x=2 and y=-1

This problem is a good reason to practice the simple
products:

x^2 - y^2 is a difference of two squares and it
returns the product (x-y)(x+y)

We'll replace x and y by the
given values and we'll get:

(x^2 - y^2)^2 = [(x-y)(x+y)]^2
= [(2+1)(2-1)]^2 = [(3)*(1)]^2 = 3^2 = 9

We could also
expand the binomial using the formula:

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

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

We'll replace x and y by the given values and we'll
get:

(x^2 - y^2)^2 = 2^4 - 2*4*1 + 1 = 16 - 8 + 1 = 8+1 =
9

Therefore, the value of the given
expression is 9.