Exercise 59 Page 62

To factor the given expression, we will use the difference of squares pattern. a^2- b^2=( a- b)( a+ b) Let's write it in a^2-b^2 form and factor. x^(16)-81 & = ( x^8)^2- 9^2 &=( x^8- 9)( x^8+ 9) Notice that x^8-9 is also a difference of squares. We need to apply the technique one more time. x^8-9 & = ( x^4)^2- 3^2 &=( x^4- 3)( x^4+ 3) Since 3 is not a perfect square, (x^4-3) is not a difference of squares. We will now replace x^8-9 with its factored form. x^(16)-81 & = (x^8-9)(x^8+9) & = (x^4-3)(x^4+3)(x^8+9)