Chapter 7 - Polynomial Equations and Factoring - 7.7 - Factoring Special Products - Exercises - Page 401: 23

Error $=(n-8)^2$ Correct solution $=(n+8)(n-8)$

The given polynomial is $= n^2-64$ Write the polynomial as $a^2-b^2$. $= n^2-8^2$ Use difference of two square pattern $a^2-b^2=(a+b)(a-b)$. We have $a=n$ and $b=8$. $= (n+8)(n-8)$ Hence, the error is $(n-8)^2$ and the correct solution is $(n+8)(n-8)$.