Question

What is the complete factorization of r2 - 6r - 9s2 + 9? A) (r - 3 + 3s)(r - 3 - 3s) B) (r + 3 + 3s)(r - 3 - 3s) C) (r - 3 + 3s)(r - 3 + 3s)

Answer 1

$r^2-6r-9s^2+9=r^2-6r+9-9s^2=r^2-2\cdot r\cdot3+3^2-9s^2\\\\\text{use}\ (a-b)^2=a^2-2ab+b^2\\\\=(r-3)^2-9s^2=(r-3)^2-(3s)^2\\\\\text{use}\ a^2-b^2=(a-b)(a+b)\\\\=(r-3-3s)(r-3+3s)\to A$