Question:
Factorize each of the following algebraic expression:
x2 − y2 + 6y − 9
Solution:
$x^{2}-y^{2}+6 y-9$
$=x^{2}-\left(y^{2}-6 y+9\right)$
$=x^{2}-\left(y^{2}-2 \times y \times 3+3^{2}\right)$
$=x^{2}-(y-3)^{2}$
$=[x-(y-3)][x+(y-3)]$
$=(x-y+3)(x+y-3)$
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