Question:
Factorize each of the following algebraic expression:
x2 + 9y2 − 6xy − 25a2
Solution:
$x^{2}+9 y^{2}-6 x y-25 a^{2}$
$=\left(\mathrm{x}^{2}-6 \mathrm{xy}+9 \mathrm{y}^{2}\right)-25 \mathrm{a}^{2}$
$=\left[\mathrm{x}^{2}-2 \times \mathrm{x} \times 3 \mathrm{y}+(3 \mathrm{y})^{2}\right]-25 \mathrm{a}^{2}$
$=(\mathrm{x}-3 \mathrm{y})^{2}-(5 \mathrm{a})^{2}$
$=[(\mathrm{x}-3 \mathrm{y})-5 \mathrm{a}][(\mathrm{x}-3 \mathrm{y})+5 \mathrm{a}]$
$=(\mathrm{x}-3 \mathrm{y}-5 \mathrm{a})(\mathrm{x}-3 \mathrm{y}+5 \mathrm{a})$