Question

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

Answer 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

Answer 2

x^4 - 2x^2 +1

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