Fine the product mentally. [ (x+1) (x-1) ^2

x^4 - 2x^2 + 1

Step-by-step explanation:

[ (x+1) (x-1) ]^2

We notice that this is the difference of squares

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

Since we have (x+1) (x-1), it simplifies to (x^2 - 1)

[x^2-1]^2

We know (a-b) ^2 is a^2 - 2ab + b^2

[x^2-1]^2 = x^4 - 2x^2 + 1

If the product is: [ (x+1) (x-1) ]^2, the answer is:

[ (x+1) (x-1) ]^2 = [x^2-1]^2 = x^4-2x^2+1