Question

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

Answer 1

\[x^2 - y^2 + 6y - 9\]
\[ = x^2 - ( y^2 - 6y + 9)\]
\[ = x^2 - ( y^2 - 2 \times y \times 3 + 3^2 )\]
\[ = x^2 - (y - 3 )^2 \]
\[ = [x - (y - 3)][x + (y - 3)]\]
\[ = (x - y + 3)(x + y - 3)\]