Chapter R - Review of Basic Concepts - R.4 Factoring Polynomials - R.4 Exercises - Page 44: 106

(q + p + 3)(q - p + 3)

$q^2$ + 6q + 9 - $p^2$ = $q^2$ + 2 * 3 * q + $3^2$ - $p^2$ Now, $a^2$ + 2 * a * b + $b^2$ = $(a + b)^2$ and a = q , b = 3 Which implies, = $(q+3)^2$ - $p^2$ Now, $a^2$ - $b^2$ = (a+b)(a-b) and a = q+3, b = p Which implies, = ((q+3) + p)((q+3) - p) = (q + p + 3)(q - p + 3) which is the answer