Question

Factorize each of the following algebraic expression:
x² − y² + 6y − 9

Answer 1

$$\begin{gathered} x^2-y^2+6y-9 \\ =x^2-(y^2-6y+9) \\ =x^2-(y^2-2\times y\times 3+3^2) \\ =x^2-(y-3{)}^2 \\ =[x-(y-3)\left]\right[x+(y-3)] \\ =(x-y+3\left)\right(x+y-3) \end{gathered}$$